The elastic boundary integral equation (BIE) method is one of the family of boundary element procedures in use today. Its basis is derived simply in terms of influence functions. These functions may involve completely general geometry modeling capability or may include special features (e.g., crack) for improved accuracy. A simple review of these points is given in terms of the beam problem.Application of the BIE methodology is given for a series of 2D stress analyses and fracture mechanics analysis problems, as well as for a significant 3D stress concentration problem. The results show the ease of use and accuracy of this methodology.