The problem of a flow of conducting fluid in the initial part of a plane channel in transverse magnetic field is solved analytically using Oseen and inductionless approximations. A typical assumption for the solution of similar problems by means of the Oseen approximation is that the velocity and the pressure of the fluid are given at the entrance of the channel. These boundary conditions overdetermine the problem. In the present paper the analytical solution of the problem is obtained with the condition that only the velocity of fluid flowing into the channel through the channeĺs lateral side is given. The problem was solved analytically by means of the Fourier transform. Numerical calculations give the M-shaped velocity profiles in the entrance region of the channel at large Hartman numbers. Dependence of the length of the initial part Linit on the Hartman number is analyzed.