  In this paper, we initiate a new study of steady funnel-flow accretion onto
strongly magnetized neutron stars, including a full treatment of shock
generation. As a first step, we adopt a simplified model considering the flow
within Newtonian theory and neglecting radiative pressure and cooling. The flow
is taken to start from an accretion disc and then to follow magnetic field
lines, forming a transonic funnel flow onto the magnetic poles. A standing
shock occurs at a certain point in the flow and beyond this material accretes
subsonically onto the star with high pressure and density. We calculate the
location of the standing shock and all other features of the flow within the
assumptions of our model. Applications to observed X-ray pulsars are discussed.
