The Mack-Wolfe test is the most frequently used non parametric procedure for the umbrella alternative problem. In this paper, modifications of the Mack-Wolfe test are proposed for both known peak and unknown peak umbrellas. The exact mean and variance of the proposed tests in the null hypothesis are also derived. We compare these tests with some of the existing tests in terms of the type I error rate and power. In addition, a real data example is presented.