Induction coil gun uses electromagnetic forces to accelerate metallic tubular projectiles for impact studies. It consists of a helical coil and a cylindrical projectile placed coaxially with the coil. Electromagnetic flux linkage between the coil and the projectile sets up axial and radial forces on the projectile. The axial force accelerates the projectile out of the coil, while the radial force leads to pinching. In certain experiments, projectiles are non-uniformly pinched and undergo plastic buckling. This is manifested in longitudinal cracks that degrade system efficiency. These cracks cannot be handled in a R-Z axisymmetric model. Hence we have developed a composite model consisting of MHD R-Z (axisymmetric) and 2D-Hydrodynamic X-Y (plane geometry) models to study deformation and longitudinal cracking. Our study predicts that an initial perturbation in projectile thickness along the Θ direction can grow and lead to localization of plastic strains causing longitudinal cracking.