Estimation of uniaxial compressive strength (UCS) by P-wave velocity (V_P) is of great interest to geotechnical engineers in various design projects. The specimen diameter size is one of the main factors that influence rock parameters such as UCS and V_P. In this study, the diameter size of specimens that effect UCS and V_P is investigated. Moreover, the correlation between UCS and V_P are examined via empirical analysis. For this purpose, 15 travertine samples were collected and core specimens with a diameters size of 38, 44, 54, 64 and 74 mm were prepared. Then, uniaxial compressive strength and P-wave velocity tests were conducted according to the procedure suggested by ISRM (1981). It is concluded that the diameter size of the specimen has a significant effect on UCS and V_P. Moreover, it was found that the best correlation between relevant parameters obtained for the specimen diameter of 38 mm.