Spatial derivative of elastic parameters causes error in the reflection and transmission coefficients in the heterogeneous finite difference formulation due to smoothing over one grid spacing at the interfaces. The first order hyperbolic equation, free from spatial derivative of elastic parameters and divergence, has been solved for SH-wave using the Lax-Wendroff scheme for an inhomogeneous medium. The scheme allows course sampling and fast fluctuations in medium parameters and also behaves well at the discontinuities of elastic parameters. The present work has concentrated on the numerical solution and computational procedure for the SH-wave simulation. A relevant computer program package has been developed and implemented for the modelling of cross-well geometry and hard rock terrain overlain by a weathered layer.