We introduce a numerical methodology to compute the solution of an adhesive normal contact problem on rough surfaces with the Boundary Element Method. Based on the Fast Fourier Transform and the Westergaard’s fundamental solution, the proposed algorithm enables to solve efficiently the constrained minimization problem: the numerical solution strictly verifies contact orthogonality and the algorithm takes advantage of the constraints to speed up the minimization. Comparisons with the analytical solution of the Hertz case prove the quality of the numerical computation. The method is also used to compute normal adhesive contact between rough surfaces made of multiple asperities. © 2017, Springer-Verlag Berlin Heidelberg.