Although sounding the shofar is a great mitzvah, for by doing so we proclaim G‑d's sovereignty and we also stir up His mercy on behalf of all those who face Divine judgment, nonetheless, the Sages ordained that if Rosh Hashanah falls on Shabbat, the shofar is not sounded.

Their ruling was based on the stringency of the Shabbat laws, for it is possible that the one sounding the shofar might not be expert in doing so and would go and consult one who is expert to either teach him or sound the shofar for him. He may thus come to either transgress the prohibition of carrying [the shofar] four amos in a public area or of transferring it from domain to domain. We thus see that the severity of the laws of Shabbat are such that the possibility of one person transgressing is deemed more important than sounding the shofar on behalf of the entire community. And the same applies even if there is an eruv [where carrying is permitted] or even if there is no area that fits the criteria of being a public domain according to Torah law.

It should be noted, however, that the sounding of the shofar on Rosh Hashanah is never totally nullified, for as we have seen, the two days of Rosh Hashanah are considered to be one extended day. Thus, if the first day of Rosh Hashanah falls on Shabbat, we still sound the shofar on the second day of Rosh Hashanah and it is as if it were sounded on the first day. The second day of Rosh Hashanah can never fall on Shabbat.

The edict not to sound the shofar on Shabbat applied only to those places where there was no permanent beis din - Rabbinical court. When the Beis ha-Mikdash stood, and the Sanhedrin sat in Jerusalem, the shofar was sounded there even when Rosh Hashanah fell on Shabbat. This was true of all areas within the boundaries of Jerusalem as well. In the remainder of Israel's cities, however, the shofar was not sounded.