An apparatus includes one or more die groups which are movable independently of one another, each including a female part having a matrix cavity and a male part destined to penetrate into the cavity such as to define a forming chamber of the product, the cavity configured to contain a batch of material. The apparatus further includes a heating station having a heater to bring the plastic material to the fluid state, and a die group cooling station downstream of the heating station. The die groups are free to be cyclically inserted in the heating station and subsequently transferred to the cooling station. A thrust group is associated to a respective die group and is configured to provide a thrust for penetrating the male part into the cavity during the stage of forming the product, the thrust group being integral with the respective die-group in displacements during the operations performed.