The problem of stellar surface oscillations under the action of perturbations in the inner layers of the star is considered. A one-dimensional hydrodynamical model is adopted to describe relatively short (compared with the stellar radius) perturbations of gas in a non-stationary gravity field. The Legendre transformation technique is used to obtain exact solutions describing the star's surface oscillations. It is shown that if the perturbations in the inner layers of the star have small energy, then the extreme characteristics of the star surface oscillations (displacement and velocity) do not depend on the nonlinearity of the problem, and thus, they can be calculated in the frame-work of a linear hydrodynamical model. The criterion for breaking of the wave coming to the star's surface is obtained. It is found that this criterion can be defined by solving the linear problem and therefore having a very clear physical sense (the ratio of the wave acceleration to the acceleration due to gravity). It is shown that the variable part of the gravity field is responsible for gas oscillations as a whole, which does not influence decisively the wave dynamics of the stellar surface. The spectrum of stellar surface oscillations is calculated.