Abstract <p>A spatial problem of normal contact between an elastic wedge with a traction-free face and an infinite periodic rectilinear system of rigid punches arranged along the wedge apex (dihedral angle) is investigated. The system of punches causes an infinite normal displacement of the wedge face (particular case of a half-space). We regularize the divergent kernel of the integral equation with respect to contact pressures using an additional periodic system of normal forces acting outside the contact region. This system is parallel to the infinite row of punches and has the same period. The forces in the regularizing infinite row are equal in absolute value and directed oppositely to the forces applied to the punches. Two regularization cases are considered: the infinite row of forces is applied outside the wedge apex (the first case) or on the apex (the second case). Regularized integral equations are solved using the Galanov numerical method, allowing one to simultaneously determine the contact region and contact pressures.</p>