A comprehensive approach to the solution of various anisotropic composite laminate crack problems is presented. Based upon the complex variable formulation, several sets of stress functions are proposed for the problems of the single edge crack, the double edge crack, cracks emanating from a hole and the interaction between holes and crack. With these functions, the governing equation of anisotropic plate theory, the single valuedness displacement condition and stress-free conditions along the crack can be satisfied automatically, while boundary conditions are approximately satisfied by means of the boundary collocation method in the least square sense. Results obtained here are satisfactory in comparison with existing solutions.