In this research a new method has been proposed for finite element analysis of three dimensional problems with incompressible materials using linear tetrahedral elements. Nowadays it is well understood that numerical one-field models formulated by such elements do not satisfy Babu?ka-Brezzi criteria. The method presented in this thesis is based on removing volumetric modes from the displacement/velocity fields in an iterative manner. To this end, a set of nodal forces are calculated with the aid of appropriate control volumes. The control volumes are constructed over the neighboring elements. This has been performed by considering the following forms for the control volume; (1) An edge-based control volume is defined by assembling of smaller tetrahedrals constructed by dividing the main elements. First, an auxiliary node is considered at the middle of each element and then the smaller neighboring elements, in each pair of main elements with a shared face, are assembled. The constructed control volumes do not overlap. (2) An element-based control volume is defined by assembling all neighboring elements having shared faces with a generic element. In this form, the control volumes overlap. (3) A so called “outer-node-based” control volume is defined by assembling all elements connected to a global generic node. Again in this form the control volumes overlap. (4) A so called “inner-node-based” control volume. In this form an element is divided into smaller ones so that four influence volumes are defined for the local vertex nodes. Then at each global node, the control volume is defined by assembling the influence volumes allocated to the node in all main elements connected to it. The constructed control volumes do not overlap in this form. With so defined control volumes, performance of the method is examined through the solution of a wide range of benchmark problems. The results show that the method is not sensitive to the type of the control volumes, and is very efficient in modeling the incompressibility effect.