Abstract: An electromechanical brake pressure generator including a spindle drive unit for converting a rotational motion of an electric motor-driven drive shaft into a translatory motion of a piston that is coupled to the spindle drive unit, the spindle drive unit being operatively connected to the drive shaft via a multi-stage transmission. The multi-stage transmission is a planetary gear set having a first and a second stage. With the aid of the transmission, a spindle or a spindle nut of the spindle drive unit is drivable, which is rotatably mounted in a housing of the brake pressure generator via a bearing assembly receiving axial and radial forces. A braking system for a vehicle including an electromechanical brake pressure generator is also described.