Development of a reliable numerical model capturing major physical mechanisms controlling explosive welding and considering properties of all process components i.e. base plate and flyer plate is the goal of the paper. To properly replicate materials behavior under these severe conditions a meshfree approach, namely Smooth Particle Hydrodynamics (SPH), was used to discretize the computational domain. The model is based on the Mie-Gruneisen shock equation of state applied to the Ti/Cu system as a case study. Examples of results in the form of velocity, equivalent stress, equivalent strain, and pressure fields are presented within the paper.