The stress wave expressed by the double exponential function is often used as the dynamic input in the numerical analysis for blasting engineering. A solution of stress wave propagation in elastic rock based on the characteristics method is an important benchmark for engineering numerical analyses

and for the validation of a dynamic numerical algorithm. The problem of blasting wave propagation in the surrounding infinite medium is solved using the given unified approach for elastic waves based on the characteristics method. The solution procedures for the radial and circumference stresses and the velocity and displacement waves during the compression blasting wave propagation are given

and these procedures are coded in MATLAB. The results of the radial and circumference stresses and the velocity and displacement waves are discussed. The characteristics method provides a powerful tool for solving the hyperbolic partial differential equations

and the solution of compression wave

expressed by the double exponential function

plays an important role in the analysis of the wave propagation problem.