  A physical model and two-dimensional numerical method for computing the
evolution and spectra of protostellar clouds are described. The physical model
is based on a system of magneto-gasdynamical equations, including ohmic and
ambipolar diffusion, and a scheme for calculating the thermal and ionization
structure of a cloud. The dust and gas temperatures are determined during the
calculations of the thermal structure of the cloud. The results of computing
the dynamical and thermal structure of the cloud are used to model the
radiative transfer in continuum and in molecular lines. We presented the
results for clouds in hydrostatic and thermal equilibrium. The evolution of a
rotating magnetic protostellar cloud starting from a quasi-static state is also
considered. Spectral maps for optically thick lines of linear molecules are
analyzed. We have shown that the influence of the magnetic field and rotation
can lead to a redistribution of angular momentum in the cloud and the formation
of a characteristic rotational velocity structure. As a result, the
distribution of the velocity centroid of the molecular lines can acquire an
hourglass shape. We plan to use the developed program package together with a
model for the chemical evolution to interpret and model observed starless and
protostellar cores.
