The machine for packaging groups of products in a wrapping sheet, includes a device for spreading a wrapping sheet and a handling device, adapted to reciprocally move a group of products to be packaged and the wrapping sheet, so as to wrap the wrapping sheet around the group of products as a result of the reciprocal movement between the wrapping sheet and group of products. The machine further includes temporary support members adapted to support flaps of the wrapping sheet protruding with respect to the group of products during a step of reciprocal movement between the group of products to be packaged and the wrapping sheet.