An extensive theoretical treatment is presented of the problem of plane progressive sound waves (simple waves) produced by continuous, high‐amplitude motion of a piston in a lossless, semi‐infinite tube. The fluid in the tube is assumed to be nondissipative; liquids as well as perfect gases are considered. The analysis is given in both Eulerian and Lagrangian coordinates. Earnshaw's exact solution in parametric form is first given for arbitrary piston motion. Special attention is then given to the case of sinusoidal piston motion. Approximate but explicit power‐ and Fourier‐series solutions for this case are derived from the exact solution. Alow‐amplitude nonlinear theory of simple wavesis proposed. In this theory nonlinear effects are considered in a simple yet general manner.A brief analysis of shock formation is also given. It is shown that the generally accepted formula for the distance at which the shock forms when the piston motion is sinusoidal is rigorously correct only under very special circumstances.