A solution of an orthotropic elastic plane problem is derived for a frictional rigid flat punch on a half plane with an oblique edge crack. A mapping function is used for arbitrary configurations. No stress function using a mapping function seems to have been derived. The problem is solved as a Riemann–Hilbert problem. The final exact stress functions are represented by an irrational mapping function as a closed form. Stress components are represented by one complex variable. Arbitrarily shaped half plane problems can be solved by exchanging the mapping function. Therefore, once the analytical solution has been derived, calculating the stress components is simpler than for an isotropic problem. It is easier to use an irrational mapping function than to form a rational mapping function for an isotropic problem. As an example, the stress distributions are shown for a frictional coefficient and an oblique edge crack angle. Four elastic constants are expressed by two independent parameters.