A thin, truncated conical shell is analyzed for the initial transient response due to the passage of a pressure front of constant velocity and amplitude. The principle of virtual work is applied to a segment of the shell, between two adjacent generatrices, treated as a beam on an elastic foundation. The ends of the shell are considered to be simply supported. The natural or free modes of vibration are approximated using an 8‐term series of functions each satisfying the boundary conditions, and the resulting modes are used in conjunction with time‐dependent coefficients to formulate the forced response.