A slip form paver machine includes a slip form mold and left and right side form assemblies closing the slip form mold on the sides. Each side form assembly includes a mounting portion, a side form, and a side form actuator configured to move the side form up and down relative to the mounting portion to adjust a height of the side form relative to the ground surface. At least one side form height sensor is configured to detect the height of the side form. A controller is configured to receive input signals from the side form height sensors and to send control signals to the side form actuators to control the height of the side forms relative to the ground surface.