The atmospheric pressure effects on the nutations are evaluated using the analytical expression of the rotational motion of the Earth in inertial space as a function of the external surface pressure torque. The most efficient term in perturbing the nutations is the S1 solar barometric tide of thermal origin; this wave induces a contribution to the prograde annual nutation but seasonal modulations of S1 may also cause perturbations to other nutations. Two extreme cases of oceanic response to pressure fluctuations are considered (inverted barometer ocean or non-inverted barometer ocean) and various kinds of figures (ellipsoid, geoid, topography) are introduced in the pressure torque computation. According to the forcing amplitude of the pressure field and to various assumptions in the torque computation, we obtain contributions to the nutation values ranging from a few tenths of a milliarcsecond up to several milliarcseconds for the semi-annual and annual terms. This shows the importance of atmospheric pressure corrections which have been ignored until now in the theoretical expressions of nutations as well as in the set of corrections applied to the observed nutations.