A process for obtaining a container of a given shape from sheet material, comprising the steps of: - providing a sheet; - providing a mould having a forming cavity, which defines a reference axis and has a shape corresponding to said given shape of said container; - positioning said sheet over said forming cavity; - providing a forming device having forming means (41, 42) arranged on the side of said sheet opposite to said forming cavity, and operating said forming means for inserting said sheet into said forming cavity to deform it until a container blank is obtained having a shape approximating said given shape; and - blowing a gas under pressure into said forming cavity to deform said container blank until said container with said given shape is obtained; wherein said step of inserting said sheet into said forming cavity includes: - setting in contact with said sheet a first operating surface of a forming member (41, 42) and pushing by means of said first operating surface said sheet into said forming cavity, for a first stretch along said reference axis; and - further pushing said sheet into said forming cavity by means of a second operating surface of a forming member (41, 42), which is of smaller size than said first surface, for a second stretch along said reference axis, characterized in that said forming device comprises a first forming member and a second forming member that can be driven along said reference axis separately or simultaneously, said process including: - setting said first and second forming members (41, 42) substantially in one and the same position along said reference axis so that they define together said first operating surface; - in this condition, feeding said first and second forming members (41, 42) in a fixed way with respect to one another along said reference axis, for said first stretch; and - keeping said first forming member stationary and further feeding said second forming member along said reference axis, for said second stretch, one end of said second member defining said second operating surface. - providing a sheet; - providing a mould having a forming cavity, which defines a reference axis and has a shape corresponding to said given shape of said container; - positioning said sheet over said forming cavity; - providing a forming device having forming means (41, 42) arranged on the side of said sheet opposite to said forming cavity, and operating said forming means for inserting said sheet into said forming cavity to deform it until a container blank is obtained having a shape approximating said given shape; and - blowing a gas under pressure into said forming cavity to deform said container blank until said container with said given shape is obtained; - setting in contact with said sheet a first operating surface of a forming member (41, 42) and pushing by means of said first operating surface said sheet into said forming cavity, for a first stretch along said reference axis; and - further pushing said sheet into said forming cavity by means of a second operating surface of a forming member (41, 42), which is of smaller size than said first surface, for a second stretch along said reference axis, said forming device comprises a first forming member and a second forming member that can be driven along said reference axis separately or simultaneously, said process including: - setting said first and second forming members (41, 42) substantially in one and the same position along said reference axis so that they define together said first operating surface; - in this condition, feeding said first and second forming members (41, 42) in a fixed way with respect to one another along said reference axis, for said first stretch; and - keeping said first forming member stationary and further feeding said second forming member along said reference axis, for said second stretch, one end of said second member defining said second operating surface. - setting said first and second forming members (41, 42) substantially in one and the same position along said reference axis so that they define together said first operating surface; - in this condition, feeding said first and second forming members (41, 42) in a fixed way with respect to one another along said reference axis, for said first stretch; and - keeping said first forming member stationary and further feeding said second forming member along said reference axis, for said second stretch, one end of said second member defining said second operating surface.