Abstract: A process to manufacture a cylinder for a rotary hermetic compressor having a rolling piston, of the type presenting a substantially cylindrical tubular body (20) which defines a pair of opposite end faces (21,22) that are parallel to each other; an internal cylindrical wall (23); and an external wall (24) which is spaced away from said internal cylindrical wall (23), said cylinder further presenting a radial vane slot (10) which is provided from said internal cylindrical wall (23), includes the steps of:a) shaping in a unique blank piece a substantially cylindrical tubular body (20);b) providing tension concentration zones in the cylindrical tubular body (20), so as to define a weakening line according to a partitioning diametral plane which passes through the cylinder part that is going to receive the vane slot (10).