A method for analyzing strong cylindrical blasts in cases where the source mass is not negligible is presented. Analytic expressions for the shock position as a function of time and shock speed and pressure as functions of position are derived. An approximation to classical Taylor–Sedov theory is extended to the near‐field regime where the source mass is not negligible. Results from example calculations are compared to Taylor–Sedov theory as well as thermodynamic free expansion. ©1995 American Institute of Physics.