This study examines the vibratory characteristics of rectangular membranes having an outer rounded-edges periphery. This class of membranes with rounded outer corners has a great advantage over membranes with a rectangular platform wave propagation at the boundary being greatly diffused. As a result, such membranes have a great potential for use in practical engineering applications, especially in waveguides-based structures. Based on an effective 2D Differential-Quadrature numerical method, the frequencies and respective modeshapes of a rectangular membrane with rounded-edges are computed. This method is shown to yield better versatility, efficiency and less computational execution than other discretization methods. The simulated results, showing complex mode exchanges occurring for the higher order modes, demonstrate advantageous use for such membrane patterns in the design of tunable waveguides.