A pumping apparatus has a peristaltic drive device for pumping a medium through a line that has a compressible portion. The pump contains a one-piece shaft with offset cam segments and lamellae. The shaft may or may not include a core shaft or a continuous core region for an increase in stability. The continuous core region has cam segments offset with respect to one another and contiguous to one another. The ratio between the height and stroke of the lamellae is about 4:1 or less.