Distribution-free tests are proposed to test the homogeneity of k-samples against umbrella alternatives when the point of umbrella is known. The tests are simple to compute and hence are useful for practical purposes. They are based on two-sample Mann-Whitney U-statistics and can be treated as the competitors to a test due to Mack and W olfe. The distributional properties of the tests have been derived and their performances in terms of Pitman asymptotic relative efficiency are discussed.