We numerically investigate the gravitational collapse of rotating magnetic protostellar clouds. The simulations are performed using 2D MHD code 'Enlil'. The code is based on TVD scheme of increased order of accuracy. We developed a model of the initially non-uniform cloud, which self-consistently treats gas density and large-scale magnetic field distribution. Simulation results for the typical parameters of a solar mass cloud are presented. In agreement with our previous results for the uniform cloud, the isothermal collapse of the non-uniform cloud results in formation of hierarchical structure of the cloud, consisting of flattened envelope and thin quasi-magnetostatic primary disk near its equatorial plane. The non-uniform cloud collapses longer than the uniform one, since the magnetic field is dynamically stronger at the periphery of the cloud in the former case.