The inertial migration of particles in a dilute suspension flow through the entry region of a plane channel (or a circular pipe) is considered. Within the two-fluid approach, an asymptotic one-way coupling model of the dilute suspension flow in the entry region of a channel is constructed. The carrier phase is a viscous incompressible Newtonian fluid, and the dispersed phase consists of identical noncolloidal rigid spheres. In the interphase momentum exchange, we take into account the drag force, the virtual mass force, the Archimedes force, and the inertial lift force with a correction factor due to the wall effect and an arbitrary particle slip velocity. The channel Reynolds number is high and the particle-to-fluid density ratio is of order unity or significantly larger unity. The solution is constructed using the matched asymptotic expansion method. The problem of finding the far-downstream cross-channel profile of particle number concentration is reduced to solving the equations of the two-phase boundary layer developing on the channel walls. The full Lagrangian approach is used to study the evolution of the cross-flow particle concentration profile. The inertial migration results in particle accumulation on two symmetric planes (an annulus) distanced from the walls, with a nonuniform concentration profile between the planes (inside the annulus) and particle-free layers near the walls. When the particle-to-fluid density ratio is of order unity, an additional local maximum of the particle concentration on inner planes (an inner annulus) is revealed. The inclusion of the corrected lift force makes it possible to resolve the nonintegrable singularity in the concentration profile on the wall, which persisted in all previously published solutions for the dilute suspension flow in a boundary layer. The numerical results are compared to the tubular pinch effect observed in experiments, and a qualitative analogy is found.