In this work a momentum source model is provided to describe the flow pattern of an incompressible fluid with a magnetic field. A restricted class of analytical solutions for a one‐sided jet, a two‐sided symmetric jet, and a two‐sided asymmetric jet are obtained. Four kinds of analytical solutions for a two‐sided jet are classified by the jet cone angle which depends on two parameters related to the Alfve´nic Mach number and the momentum flux. The cone angle and the boundary between the two sides of a two‐sided asymmetric jet are determined by the ratio of the momentum flux parameters on each side. From this model the mass flux, momentum flux, and energy flux entrained by the jet are calculated and the differences between the above properties on each side of a two‐sided asymmetric jet are obtained as well. The rotation of the jet and the restrictions of incompressibility are discussed.