A previously developed direct boundary element method for analyzing stresses around pin-loaded holes of composite laminates has been extended with a refined and improved computational algorithm. The method, procedure, and computer program are verified by elasticity solutions in polar coordinates for eyebars and plates having an open, as well as loaded, hole. In turn, boundary tractions generated by the direct boundary element method allowing direct application of elasticity solutions are presented. Such a scheme, which couples the boundary element and analytical methods, appears to be plausible, accurate, and efficient for practical applications.