Using an analytical description of the profile of the indexes of refraction of birefringent Ti:LiNbO3channel waveguides, a very fast method was developed to compute the optical mode field distributions. Using these results, field overlap integrals were evaluated to calculate the pump threshold power of integrated optical parametric oscillators with Ti:LiNbO3channel waveguides. A variation of the guide parameters enabled the determination of optimized profiles yielding minimum oscillation threshold. The pump threshold power of doubly and singly resonant structures was evaluated as a function of the resonator parameters, waveguide losses, mirror reflectivities, and device length. In the doubly resonant configuration, threshold powers lower than 10 mW can be expected.