A tangential milling cutting insert has two identical opposing end surfaces with two identical opposing major side surfaces of a generally parallelogrammatic shape and two identical opposing minor side surfaces extending between them. An ambidextrous tangential cutting insert has two non-identical end surfaces and two opposing major side surfaces of a generally trapezoidal nature. In either cutting insert, each end surface has a peripheral cutting edge and four corners of which two diagonally opposed corners are lowered and the other two are raised. Each end surface comprises four separate planar regions arranged in pairs, the planar regions do not protrude relative to the surrounding end surface and the two planar regions of a given pair of planar regions slope in opposite directions with respect to a median plane of the cutting insert.