Eulerian numerical technique is superior to the Lagrangian method in the calculation of problems involving shocks and large deformations. However, the Eulerian method has its own several technical problems that are being improved presently. A major one of those is the numerical diffusion related to the computational scheme ; another is the determination of pressures in mixed cells when problems include two or more types of materials. The cubically interpolated polynomial (CIP) scheme exhibits its advantages to the prevention of numerical diffusion. For the pressures in mixed cells, a relatively simple method has recently been proposed for solving the interactions of materials with solid and gaseous phases. The method explicitly solves pressures in mixed cells without use of the iteration procedures. This paper will describe the development of a two - dimensional Eulerian code, MARS2D (Multi - dimensional Analysis Code for Reactive Shocks, 2D vision), that employs the above two technical routines for the purposes of calculating the problems involving strong shocks and reactive media. Problems of high - velocity impact. blast waves in air, and cylinder expansion test will be taken as the computational examples.