Abstract: A peristaltic pump uses a length of elastic tube with an inlet at one end and an outlet at the second end for delivering fluid material an outlet pressure greater than the inlet pressure. A support element disposed along the length of elastic tube is in contact with the elastic tube. A mechanism moves a compression element into engagement with a segment of the elastic tube thereby forming a compressed segment with a tube center section and two folded tube edges wherein at least one surface engaging the folded tube edges has a contours that reduce stresses in the elastic tube walls at the folded tube edges increasing pump performance and/or life of the elastic tube.