Abstract This study investigates transient magnetohydrodynamic axial flow of an incompressible, viscous, electrically conducting Newtonian fluid through a porous annulus bounded by two stationary concentric cylinders. The flow is driven by a constant axial pressure gradient and subjected to a uniform transverse magnetic field. Darcy resistance is used to represent porous-medium drag, while the Lorentz-force term accounts for magnetic damping under the low-magnetic-Reynolds-number approximation. The governing momentum equation is non-dimensionalized and solved using the Laplace transform method, with numerical inversion performed by the Riemann-sum approximation. Steady-state expressions for velocity and wall shear stress are also obtained for comparison with the large-time behaviour of the transient solution. The results show that magnetic and porous resistances combine through . Increasing the Hartmann number reduces the axial velocity, while increasing the Darcy number enhances the flow by reducing porous resistance. The transient velocity and skin friction approach their steady-state limits as time increases. The formulation may be useful for idealized studies of hydromagnetic transport in porous annular systems. Keywords: Magnetohydrodynamics; porous annulus; transient axial flow; Darcy number; Hartmann number; Laplace transform; Riemann-sum approximation; skin friction; annular flow.