A top surface of an elevating stand of a pet feeding system defines bowl receptacles into which respective food and water bowls may be removably installed. A first zone of the top surface of the stand includes an upwardly convex ring that laterally surrounds a respective bowl receptacle. A second zone of the top surface of the stand laterally surrounds the first zone, except as interrupted by a finger notch. Each bowl has a peripheral lip with a lower surface formed as a downwardly concave ring that fits over the upwardly convex ring of the stand. An edge of the bowl rests on the second zone at a location below the upper limit of the convex ring. A base of the stand cooperates with upstanding ribs in an elastomeric mat to prevent lateral movement of the stand and to prevent rotation of the stand around the stand center.