Saying Tehillim in Davening
Before Birkas HaTorah
1. One should not say pesukim before Birkas HaTorah even if they are said as a plea [“derech tachanunim”]. Some say it is not a problem if they are just pleas, but it is proper to satisfy the first opinion (שו''ע או''ח סי' מ''ו ס''ט ). The Rama writes that the minhag follows the second opinion (רמ''א שם ). According to the present minhag to say Birkas HaTorah right after Asher Yatzar, before anything else, one should not say any pesukim beforehand, even if they are said as pleas (מ''ב סקכ''ז וכ''ח ).
2. Tehillim. Therefore, if someone says Tehillim before Shacharis, he should lechatchilah say Birkas HaTorah first. However, if someone does not go back to sleep when he wakes up in the middle of the night without saying some Tehillim first, he may say Tehillim without saying Birkas HaTorah (שו''ת מנחת יצחק ח''ח סי' ה').
In Pesukei Dezimrah
3. After starting Boruch She’amar, one must be careful not to speak until the end of Shmoneh Esrei (שו''ע נ''א ס''ד ). Also, one may not say maamados (ע' סדר מעמדות בסדר רב עמרם גאון ) or requests during Pesukei Dezimrah (באר היטב סק''ג ). Therefore, one should also refrain from saying Tehillim during Pesukei Dezimrah or before Yishtabach. Although Pesukei Dezimrah itself is Tehillim, Chazal established the nusach with extreme precision, and we should not add to what they established (חיד''א, מורה באצבע סי' ג' אות ע''ד ). One may say perakim of Pesukei Dezimrah or the Shabbos/Yom Tov additions if he did not say them where they belong (אג''מ או''ח ח''ב סי' ט''ז ).
4. After Yishtabach. One may not interrupt after Yishtabach (שו''ע סי' נ''ד ס''ג ). Tehillim is considered an interruption and should not be said then. However, one may say parts of Pesukei Dezimrah he skipped.
Shmoneh Esrei
5. After the silent Shmoneh Esrei. One may not learn before taking his three steps back since he is still standing before the King. Still, one may say Tehillim since it is also a tefillah (הגר''ח קנייבסקי, אשי ישראל פל''ב הע' ע''ג ). One may certainly say Tehillim after taking his three steps back.
6. Chazoras Hashatz. One should be silent, concentrate on the brochos the chazzan is saying, and answer “Amein.” Therefore, one should avoid saying tefillos or learning during Chazoras Hashatz (מ''ב סי' קכ''ד סקי''ז ); this includes saying Tehillim.
7. Chazoras Hashatz of Rosh Hashanah Mussaf. If a chazzan is drawing out Chazoras Hashatz of Rosh Hashanah Mussaf with tunes, one may say Tehillim; it is not an interruption in Shmoneh Esrei. It is also not an interruption between the tekios blown during Mussaf [“tekios deme’umad”] since Tehillim is also a form of pleas and requests (יסוד שורש ועבודה שער האיתון שער ד' ספר שופרות ).
