Press machine (13), particularly for producing mozzarellas having a substantially two-dimensional geometry, comprising a station for sorting (14) preformed balls of mozzarella (6) and obtained with a milk- based paste and a press station (15) for shaping said preformed mozzarella balls (6) in pieces of mozzarella (8) having a substantially two- dimensional geometry, said press station (15) comprising an alveolar plane (18) defining at least one alveolar seat (21) suitable for containing at least one of said preformed balls of mozzarella (6) and coming from said sorting station (14), also comprising at least one pressing element (22) that is mobile between a resting position, wherein said pressing element (22) is located distant from said alveolar plane (18) for arranging said preformed ball of mozzarella (6) in said alveolar seat (21), and a pressing position, wherein said pressing element (22) is located above said alveolar seat (21) for pressing said preformed ball of mozzarella (6). Furthermore, a production process using the above press machine for producing mozzarella having a substantially two-dimensional geometry
