A calculation is made of the forces between hyperons and nucleons under the assumption that the forces are due to the exchange of pions. The Λ and Σ are assumed to have spin 1/2 and the same parity. The Hamiltonian is taken to be the same as the static-model pion-nucleon Hamiltonian except for differences in isotopic spin and possibly in the strength of the coupling. The same approximations are made as those ordinarily made in evaluating the nucleon-nucleon potential, although it is noted that in case all the pion-baryon coupling constants are equal, the hyperon-nucleon potentials are just linear combinations of the observed nucleon-nucleon potentials. The pion-hyperon coupling constant is determined by comparison with potentials obtained from analysis of hyperfragment data. The resulting value is about the same as the pion-nucleon constant. The elastic hyperon-nucleon and Λ+N<-->Σ+N scattering cross sections are evaluated. Results are consistent with experiment.