The present invention relates to an upsetting press (1, 1′) for upsetting an end (2) of a metallic material pipe (3), e.g. for petroleum applications. The press (1, 1′) comprises a supporting structure (10) which defines a working space and first locking means (15) for locking the pipe (3) to be upset. The press further comprises first upsetting means comprising at least one first upsetting die formed by a first pair of half dies (21, 22) which can be separated and closed about the end (2) of the pipe (3) to be upset and at least one axially movable cylindrical punch (30). The press (1, 1′) further comprises die holding means which support the half dies (21, 22) moving them between a closing position and an opening position. According to the invention, the die holding means are independent from said supporting structure and are transversally movable (102) between an operating position in which the half dies (21, 22) can be closed about the end (2) of the pipe (3) to be upset and at least a non-operating position such that the half dies can be washed and/or lubricated outside the working space of the press.