Abstract: Based on the mathematical programming procedure of thecontact problem with friction and using the complex potential method in theanisotropic plane theory of elasticity, an efficient approach is presentedto deal with the frictional contact of a finite anisotropic plate containingmultiple elliptical holes and cracks subjected to arbitrary loads. Thecomplementary parameters introduced to the contact boundary are expandedinto Fourier series, and the linear complementary model considering thecrack closure is obtained by means of the Faber series expansion, conformalmapping and the least square boundary collocation technique. Some examplesare given to demonstrate the validity and effectiveness of the method.Numerical results indicate that the present method enjoys many advantages suchas high accuracy, good convergence, and is convenient to be used toinvestigate effects of crack closure on the fracture parameters of structures.