The pion-Pomeranchon Regge cut is calculated from the Mandelstam diagram, using Gribov's approach. Explicit calculations are made for three representative π-exchange processes: np→pn, π−p→ρ0n, and π+p→ρ0Δ++. Pomeranchon exchange is assumed to be mediated by an isoscalar scalar σ meson. Convergence of the loop integrals is ensured by inserting form factors to relate the off-shell pion-exchange amplitudes to known on-shell behavior. Parameters in the model are the mass of the σ meson, its coupling constants, and cutoff masses in the form factors. Excellent agreement with the data is obtained over a fairly wide range of energy. The model extrapolates well to t=−1.0 GeV2 although the parameters are obtained from a fit to much smaller values of t (|t|<0.1 GeV2). Some characteristics of the πP cut can be deduced from the results. It is self-conspiratory, a feature which is essential to account for the sharp forward spike in np→pn. It does not contribute to amplitudes with unnatural parity and unnatural charge-conjugation parity in the t channel. Furthermore, the cut contribution to amplitudes with natural parity in the t channel are strong only if the amplitudes have double helicity flip in the s channel.