The proposal of an artificial bladder is still a challenge to overcome. Bladder cancer is among the most frequent cases of oncologic diseases in United States and Europe. It is considered a major medical problem once this disease has high rates of reoccurrence, often leading to the extirpation of this organ. The most refined solution to replace this organ is the ileal bladder, which consists of a neobladder made of the patient’s intestinal tissue. Unfortunately this solution presents not only functional mechanical problems, described on the literature as voiding and leaking problems, but also biological ones (i.e. bone loss, given the absorption by the intestine of substances that should be eliminated from the organism). Urged by the urological community of the Hospital Clinic de Barcelona and backgrounded by its experience in the numerical simulation of biomedical structures, the Center of Numerical Methods in Engineering (CIMNE) had the initiative to provide the research of the mechanics of the urinary bladder and the simulation of fluid structure interaction (FSI) to account for the filling and voiding of this organ with urine. The Finite Element Method (FEM) simulation of the real bladder and the comprehensive understanding of the mechanics of this organ and its interaction with urine will give the possibility to propose geometrical improvements and study suitable materials for an artificial solution to address the cases on which the bladder needs to be removed. To reach this goal, first we proceeded to the bibliographic review of mathematical models of the urinary apparatus and to a comprehensive study of the physiology and dynamics of the bladder. A review of the major urological structures, kidney, ureter and urethra, takes place. To consider boundary conditions other surrounding structures to the urinary system are also studied. In the second part of the thesis, we propose the numerical model to study the human urinary bladder. The behavior of the detrusor muscle during filling and voiding of the bladder with urine and its ability to promote the storage of urine under low pressure need to be accurately represented, requiring the implementation of a non-linear constitutive model. The mathematical model needs to be capable to simulate the mechanical variables that govern this organ and the properties of the urine. The nonlinear behavior of living tissues is implemented and validated with examples from the literature. The quasi-incompressibility property of urine and the navierstokes equations for the fluid are taken into account. The geometry of the bladder needs to be taken into account, and the implementation of a 3D computational model obtained from the computerized tomography of a cadaver male adult is considered. The data has been treated to consider boundary conditions. Two models have been conceived: one meshed with four nodes tetrahedral and another meshed with shell elements. FSI must work for the simulation of filling and voiding of the bladder. Due to the close densities of the materials the scheme used to solve fluid-structure needs to be carefully selected. The proposed numerical model and the filling and voiding analysis are finally validated with standardized urodynamic tests. The final part of the thesis, the simulation of a neobladder is presented, being the first step to simulate numerically artificial materials for bladder replacement.