An approach is presented to computing the time‐dependent force acting on a piston as a result of the velocity of an adjacent piston which may be any specified time‐dependent function. The method is based on a Green's function solution to the time‐dependent boundary‐value problem for an impulsive piston velocity motion. An asymptotic expression for the mutual radiation impedance between square pistons has been obtained using the method. A numerical approach is also presented to obtain the mutual radiation impedance coefficients from the time‐dependent solution of the boundary‐value problem. Numerical results obtained from the asymptotic expression are shown to agree with previously published numerical results and the results obtained using the numerical approach indicated in the paper. Numerical results for time‐dependent interaction forces resulting from sinusoidal piston velocities are also presented and discussed.