In this study, two computational models were developed, the first one predicts the appearance, location, and development of the mesenchymal condensation within the upper limb as it grows. Biochemical events were modeled with reaction-diffusion equations of generic molecules. The results obtained showed that patterns generated by molecules that behave as Fgf8, Fgf10 and Wnt3a, can predict the shape of the mesenchymal condensation. Simple diffusive patterns were adequate to explain the areas where sox9 is expressed and how they are affected by the shape and size of the signaling zones and the ectoderm. Furthermore, our results suggest that Grem1 and Wnt3a have the same effect on Sox9 expression, and that Tgf-β expression could be due to inhibition of RA. The second model analyze how mechanical and biochemical stimuli affect joint morphogenesis. For this, it was assumed that cartilage growth was controlled by cyclic hydrostatic stress and inhibited by octahedral shear stress. In addition, the effect of molecules that promote chondrocyte proliferation such as PTHrP-Ihh and Wnt was included. The results obtained through the model suggest that the initial morphogenesis of the elbow joint is influenced by hydrostatic stresses together with biochemical stimulation. To solve the systems of partial differential equations in both models, the finite element method was applied. It should be noted that this document also presents a conceptual background of the biological processes before and during the development of the elbow, as well as a brief mention of what the principal characteristics of the elbow is and some pathologies associated, moreover, it is also included a brief explanation of the finite element method and the solution of the elasticity and reaction-diffusion equations through this method. (Text taken from source)