Magnetohydrodynamics (MHD) is a very challenging problem which affects the stability of Poiseuille flow. Therefore, in this work we investigate the instability of an electrically conductive fluid between two parallel plates under the influence of a transverse magnetic field. We apply the Chebyshev collocation method to solve the generalised Orr–Summerfield equations to determine wave number, growth rates and spatial modes of the eigenmodes. To get the neutral curves of MHD instability, the QZ method is used. It is observed that the magnetic field has a stabilising effect on the flow and the stability increases as we increase the Hartmann number and for various wave numbers, magnetic field put down the growth of perturbation. It is concluded that effect of perturbations is little in span-wise direction for different Hartmann numbers that increase the critical values of Reynolds numbers.