Tolkien described the basic Sindarin stress patterns in The Lord of the Rings Appendix E (LotR/1116), and they are essentially the same as for Quenya (and Latin): stress falls on heavy syllable closest to the end of the word, except (a) it cannot fall on the last syllable of polysyllables and (b) cannot be further back than the third-to-last syllable. A syllable is “light” if it has a short vowel followed by no more than one consonant; it is “heavy” if it has a long vowel, a diphthong or a short vowel followed by more than one consonant. Thus:

• For disyllabic words, the stress is always on the first syllable, as in Beren [béren].
• For trisyllabic words, the stress is on the second syllable if it is heavy as in Finarfin [finárfin] and otherwise the first syllable as in Celeborn [kéleborn].
• Longer words receive the stress on the second-to-last syllable if it is heavy as in Calenardhon [kalenárðon] and third-to-last otherwise as in Edenedair [edénedair].

In these examples the accent ´ marks stress rather than length. Remember that digraphs like th, ch and dh represent a single consonant, and do not by themselves make a syllable heavy. Thus linnathon is pronounced [línnaθon] not **[linnáθon], because th is a single consonant (IPA [θ]) for purposes of pronunciation. However ph between vowels represents long [ff], and thus does make the preceding syllable heavy. Hence Araphin is pronounced [aráffin].

One unusual feature of Sindarin is that an isolated medial m is pronounced as a single [m] but still counts as long for purposes of stress:

In Sindarin ... mb became m in all cases, but still counted as a long consonant for purposes of stress (see below), and is thus written mm in cases where otherwise the stress might be in doubt (LotR/1115).

Examples include galadhremmen [galaðrémen] “tree-meshed” and rammas [rámas] “great wall” but not amon [ámon] “hill” where there is no ambiguity for stress. Technically there is never any ambiguity for stress because intervocalic m is always derived from mb or mm, so that Turamarth is pronounced [turámarθ] despite the lack of double mm. This mm is just a hint to English readers of Sindarin about proper stress, in much the same way that umlauted ë is a hint to English readers of Quenya that the e is pronounced rather than silent. Tolkien’s choice of medial m vs. mm in Sindarin words is somewhat arbitrary, possibly for purely aesthetic reasons. See the phonetic entry on how [mm] shortened for further discussion.

Tolkien never described the patterns of secondary stress for Sindarin, but we have a couple late poems that provide hints. If we assume the poem A Elbereth Gilthoniel is in iambic tetrameter, its pattern of stress is probably:

a Él|berèth | Gilthó|nièl
silív|ren pén|na mī́|rièl
o mén|el ág|lar él|enàth
na-cháe|red pá|lan-dī́|rièl
o gà|ladhrém|min én|noràth
Fanú|ilòs, | le lín|nathòn
nef áe|ar, sī́ | nef áe|aròn
a Él|berèth | Gilthó|nièl
o mé|nel pál|an-dír|ièl
le nál|lon sī́ | di’ngú|ruthòs
a tír|o nín, | Fanú|ilòs

In the above, macron ¯ marks vowel length, acute accent ´ marks primary stress, grave accent ` marks secondary stress, and | marks the iambic feet (low-high syllable pair). The above rendition requires that we have to assume the diphthong ui in Fanuilos is broken into two syllables: Fanú-ilòs, but Tolkien himself told us this was the case:

The first vowel (a and u) was in both [ae, ui] somewhat prolonged. These dipthongs were thus of a length more or less equal to the time occupied by two syllables, and are therefore occasionally employed metrically where the normal metre requires two. Fanuilos is an example both on p. 250, Vol. I, and in Sam’s invocation, Vol. II, p. 339. (RGEO/63, footnote).

Assuming the above metrical analysis is correct, it seems that Sindarin puts secondary stress on alternating syllables before and after the main stress; Welsh does something similar, except the main stress always fall on the second-to-last syllable in Welsh. Given the small sample size and comparative shortness of the example words, other rules are possible (like secondary stress on initial and final syllables removed from the main stress). However, in languages where secondary stress is independent of syllable weight, alternating stressed syllables is the most common pattern.

Another late poem, Lúthien’s Song, also seems to be iambic tetrameter.

ir Í|thil ám|men Ér|uchī̀n
menél|-vīr sī́|la dī́r|ièl
si lóth | a gál|adh lás|to dī́n
a Hī́r | Annū́n | Gilthón|ièl
le lín|non ím | Tinū́v|ièl

The second line of this poem is potentially problematic: menel-vîr síla díriel. If pronounced as two separate words, ménel-vī́r would break the iambic pattern, putting stress on the first and third syllables. Lokyt suggested that this word might instead be pronounced as if it were a compound, with the middle syllable heavy and thus stressed, restoring the iambic pattern: menélvīr. This might even be a general rule, so that pseudo-compounds like palan-diriel would have only one primary stress, and the other stresses would be secondary: pàlandírièl.

Finally, it seems that “minor” monosyllables like prepositions or short adverbs may be unstressed in a sentence. Compare long stressed sí in the first poem to short unstressed si in the second.

Conceptual Development: In the Gnomish Grammar of the 1910s there are some cryptic comments indicating that the rules for stress might have been more complicated in the earliest versions of the language:

Accentual note. Note that all plurals (nom.) accent correctly phonologically on the penult - (poetically a license is granted in case of old words, thus celbin, célebin and celébin all are found), but genitives plural [are] all propenult except the rarer ones in -aion. Thus lépthathon but leptháion, celébion, góldathon, etc. (GG/13).

Without more information, determining the details is impossible.