Uniaxial compressive strength (UCS) and elastic properties of rocks play a major and vital role for the design of any engineering structure. The specimen diameter size is one of the main factors that influencing on UCS, elasticity modulus and Poisson’s ratio (E and υ). Here, an attempt has been made to investigate the effect of specimen diameter size on UCS, E and υ. Moreover, we studied the correlation between E and υ with UCS together with the effect of specimen diameter size on them. For this purpose, 9 different travertine samples were selected and core specimens with a diameters size of 38, 44, 54, 64 and 74 mm were prepared. Then, UCS, E and υ of samples in different diameter were determined. The test results were statistically analyzed using the method of least squares regression between the different specimen diameters with UCS, E and υ. The data analysis results showed that specimen diameter size significantly affects on UCS, E and υ. Moreover, it was found that the best correlation between E and UCS was for the specimen diameter of 38 mm, whereas there is not meaningful correlation between υ and UCS.