  This paper offers the exact analytical solutions for the magnetohydrodynamic
(MHD) flow of an incompressible generalized Burgers fluid corresponding to the
second problem of Stokes in the presence of the transverse magnetic field.
Modified Darcy's law has been taken into account. The expression for the
velocity field and associated tangential stress, presented as a sum of the
steady-state and transient solutions, are obtained by means of the integral
transforms. Moreover, several figures are plotted to investigate the effects of
various emerging parameters on the velocity field. The obtained results show
that the magnitude of the velocity and boundary layer thickness significantly
reduce in the presence of magnetic field.
