We consider the problem of testing the roundness of a manufactured object using the finger probing model of Cole and Yap [1]. When the object being tested is a disk and it's center is known, we describe a procedure which uses O(n) probes and O(n) computation time. (Here n = |1/q|, where q is the quality of the object.) When the center of the object is not known, a procedure using O(n) probes and O(n log n) computation time is described. When the object being tested is a cylinder of length l, a procedure is described which uses O(ln 2) probes and O(ln 2 log ln) computation time. Lower bounds are also given which show that these procedures are optimal in terms of the number of probes used.