This text presents elastic contact analysis in two-dimensional and axisymmetric modes, using boundary element method. The solution procedure includes the effects of frictional as well as non-frictional contact between elastic bodies. The first two chapters serve as an introduction to the field and offer a bibliographic survey of various approaches for solving elastic contact problems. In Chapter 3, the boundary element formulations for two-, three-dimensional and axisymmetric problems in elasticity are derived and numerical implementation using constant and linear elements is described. In Chapter 4, two-dimensional contact analysis between an elastic body and a rigid body, and elastic bodies is discussed. In the new approach for solving elastic contact problems, boundary element analysis and contact analysis are performed separately. The approach, therefore, is easy to implement into boundary element programmes. In order to obtain accurate results, an incremental and an iterative procedure is applied. Hertz and non-Hertz problems, with and without friction contact are also studied. In Chapter 5, the approach is extended to apply axisymmetric contact analysis between two elastic rings which have a common central axis. Linear elements are employed for discretization. Internal pressure, interference between two rings and friction are taken into account. The computed results are compared with analytical solutions. This monograph on elasticity, computational mechanics and tribology is intended for researchers in the field.