The stresses occurring in the cusp of a leaflet heart-valve prosthesis, simulated by a quarter of a spherical shell with a semicircular base, have been calculated and analyzed with a view to identifying and strengthening the most vulnerable points of the prothesis. Expressions are obtained for calculating the tensile and shear stress in the cusp of the leaflet valve. A stress analysis shows that the most dangerous points are the edges of the prosthesis and the central zone. At the fixed edge the cusp may be torn away as the result of the action of the maximum shear and tensile forces. Critical points occur in the zone of transition to the free edge of the prosthesis, where the shearing force reaches its maximum value.