Publisher Summary Magnetic reconnection is accompanied by an ultra-fast release of magnetic energy which transforms into different forms such as internal plasma energy, radiation, and fast particles. For this reason reconnection processes are important for numerous applications and are used in order to explain different phenomena such as the disruptive instability in tokamak plasmas, solar flares, and substorms in the earth's magnetosphere. The accurate 3D simulation of characteristic features of magnetic reconnection requires a very dense space grid and a very little time step as a result of Courant condition. The problem of magnetic field line reconnection is closely related to the problem of the structural stability of vector fields. The change in the topology of the magnetic field is induced by perturbations imposed at the boundary of the region. This case corresponds to the regime of driven magnetic reconnection. The main difficulty in numerical solution of the three-dimensional time-dependent MHD system consists of the presence of widely disparate time scales. A very small time step which is defined by the fastest MHD process and long calculation time which is defined by the slow MHD processes are used in the chapter. The thin structure of MHD nonlinear configurations such as current sheets requires a small space step. In this chapter the explicit finite-difference scheme is used which is more convenient for the numerical parallel implementation.