In this contribution, we demonstrate a new technique for fabricating a mechanically stretchable metasurface with tunable response on an elastic polydimethylsiloxane (PDMS) membrane operating at Terahertz (THz) frequencies. The tunability of the response of the metasurface is based on the change of the physical dimensions of individual micro-structures due to the strain caused by mechanical stretching. The technique is fast, easy and uses high resolution e-beam patterning in contrast to established screen-printing and other techniques reported in literature. Furthermore, the change in the response of the device shows linear dependence with strain over a broad range of strain with high repeatability. Thus, this technique has high potential for applications in communications technology, remote strain sensing and biological applications.