A new method for the free‐vibration analysis using the boundary element technique is presented. The method utilizes a fictitious vector function to approximate the inertia forces and then uses the well‐known concept of complementary functions and particular integrals to solve the resulting governing differential equations. The necessary particular integrals are defined for the two and three‐dimensional analyses, and the present formulation is applied to a number of two‐dimensional problems to show its accuracy and efficiency in the solution of realistic engineering problems.