The paper presents biomechanical analyses of anatomical structures and blood flow, involving the use of the computer-based finite element method. In presenting the various problems, the mechanics-based peculiarities of the problems (such as the nature of geometric and material nonlinearities) that make them conducive to finite element analysis are outlined, the computational features of the finite element method are presented and the physiological significances of the results are stressed. The first part of the paper, dealing with finite element analyses of anatomical structures and organs, concerns analyses of the arteriole, artery, heart valve, left ventricle, lung, corneo-scleral shell and the femur; herein, we are interested in determination of the material properties of the structural components of the organs, the stress states and their applications to characterization of disorders, pathologies and prostheses design. The second part of the paper, dealing with blood flow phenomena, concerns analyses of blood flow in the entrance region, at bifurcation, around inserted catheters with a view to delineate some fluid mechanical causative factors for atherosclerosis and the influence of catheter diameters on injuries to blood vessel intima.