Non-destructive methods such as ultrasonic wave velocity are extensively used for estimating physical and mechanical properties of rock due to the simplicity, economical, fast and harmless nature. Rock constructions have been made worldwide from past to present. Determination of strength of rock constructions such as archeological evidence is not possible using conventional rock strength tests. Developing a cheap, simple, non-destructive, efficient and accurate method to estimate the strength of such constructions can be useful. Rock blocks and constructions have various shapes and sizes. Rock blocks having various shapes and sizes have been prepared from marble, travertine, granite, and limestone and ultrasonic wave velocity at various directions of the blocks dimensions and the uniaxial compressive strength of cylindrical core obtained from the blocks have been measured. The results show that shapes and sizes have no effect on the ultrasonic wave velocity. At the end relationships between uniaxial compressive strength and ultrasonic wave velocity have been determined. The uniaxial compressive strength of blocks and rock constructions can be estimated by the obtained relationships using non-destructive, simple and indeed low cost method of ultrasonic wave velocity.