Magnetic resonance-guided high intensity focused ultrasound (MR-HIFU) is a noninvasive thermal technique that enables rapid heating of a specific area in the human body. Its clinical relevance has been proven for the treatments of soft tissue tumors, like uterine fibroids, and for the treatments of solid tumors in bone. In MR-HIFU treatment, MR-thermometry is used to monitor the temperature evolution in soft tissue. However, this technique is currently unavailable for bone tissue. Computer models can play a key role in the accurate prediction and monitoring of temperature. Here, we present a computer ray tracing model that calculates the heat production density in the focal region. This model accounts for both the propagation of shear waves and the interference between longitudinal and shear waves. The model was first compared with a finite element approach which solves the Helmholtz equation in soft tissue and the frequency-domain wave equation in bone. To obtain the temperature evolution in the focal region, the heat equation was solved using the heat production density generated by the raytracer as a heat source. Then, we investigated the role of the interaction between shear and longitudinal waves in terms of dissipated power and temperature output. The results of our model were in agreement with the results obtained by solving the Helmholtz equation and the frequency-domain wave equation, both in soft tissue and bone. Our results suggest that it is imperative to include both shear waves and their interference with longitudinal waves in the model when simulating high intensity focused ultrasound propagation in solids. In fact, when modeling HIFU treatments, omitting the interference between shear and longitudinal waves leads to an over-estimation of the temperature increase in the tissues.