A package for cylindrical products, particularly cigarettes or similar, this package consisting of a wrapping sheet (2) in which the cigarettes are wrapped. The wrapping sheet consists of heat-weldable plastic material and is sealed, when wrapped around a group of cigarettes (S), by the welding of parts, flaps or wings (102, 202, 402, 502, 602, 702) overlapping each other on one or more sides of the group of cigarettes (S). A vacuum or low pressure may advantageously be created inside the sealed wrapping sheet (2). A process and device for the fabrication of the package, according to which the phase of wrapping, in other words that of folding the wrapping slip (2), is executed completely in only one station to which the group of cigarettes (S) and the wrapping slip (2) are fed and in only one subsequent folding station (P), while the welding is executed in intermediate phases or in a final phase.