Using the overlapping integral method, a rib waveguide laser of monoclinic potassium double tungstate, KRE\((\text{ WO}_{4})_{2}\), co-doped with Erbium and Ytterbium has been modelled. The laser operation at 1.5 \(\upmu \)m is based on an efficient pump scheme via the energy transfer from Yb\(^{3+}\) to Er\(^{3+}\) ions. The numerical simulation requires spectroscopic parameters of the ions involved and the waveguide geometry and index profiles. This model allows determining the laser power as a function of controllable parameters such as ions doping level, pump power, cavity length or reflectance of the input/output mirrors. It has been found that, for the standard doping level used in this matrix, the optimum cavity length is only few millimeters. Overall, using simulation tools is possible to optimize fabrication parameters, and thus saving effort in the development of experimental prototypes.