This contribution describes a numerical method for the simulation of incompressible quasi-potential flows around three dimensional lifting streamlined bodies. The resulting Laplace boundary value problem is discretized using a collocation Boundary Element Method (BEM). The resolution algorithm is based on the Boundary Element Metuod library π-BEM. In the quasi-potential boundary value problem, a wake is included as a surface of discontinuity of the velocity potential. Both the potential jump and the wake surface shape are additional unknowns of the numerical problem. To evaluate the fluid velocities at the wake collocation points, needed for the wake alignment algorithm, a Hypersingular Boundary Integral Equation (HBIE) approach is adopted. A Galerkin variational formulation is used for the hypersingular BIE. Standard Gauss quadrature nodes for the external integration loop avoids integrals with singularities on the elements edges, ensuring stable evaluation.