  We present the results of 2D simulations of the magnetorotational model of a
supernova explosion. After the core collapse the core consists of rapidly a
rotating proto-neutron star and a differentially rotating envelope. The
toroidal part of the magnetic energy generated by the differential rotation
grows linearly with time at the initial stage of the evolution of the magnetic
field. The linear growth of the toroidal magnetic field is terminated by the
development of magnetohydrodynamic instability, leading to drastic acceleration
in the growth of magnetic energy. At the moment when the magnetic pressure
becomes comparable with the gas pressure at the periphery of the proto-neutron
star $\sim 10-15$km from the star centre the MHD compression wave appears and
goes through the envelope of the collapsed iron core. It transforms soon to the
fast MHD shock and produces a supernova explosion. Our simulations give the
energy of the explosion $0.6\cdot 10^{51}$ ergs. The amount of the mass ejected
by the explosion is $\sim 0.14M_\odot$. The implicit numerical method, based on
the Lagrangian triangular grid of variable structure, was used for the
simulations.
