The linearized equations for the flow of a compressible inviscid fluid in an accelerated sphere were solved for a constant step in the acceleration from a state of rest. Pressure waves whose maximum amplitude is nearly equal to the hydrostatic pressure from an equivalent steady gravitational field acting through the depth of the diameter are induced in the fluid. This maximum pressure occurs at the end of that diameter aligned in the direction of the acceleration. By means of the convolution integral, the pressure distribution on the inner surface of a sphere being accelerated sinusoidally was obtained and the reaction force resulting from the fluid motion was computed. The pressure oscillations build up in a resonant manner with amplitude linear with time when the driving‐reduced frequency is equal to an eigenvalue of the problem.