In this study, a series of triaxial tests on Jeju basalt were carried out and then rock strength parameters were estimated by the Mohr-Coulomb failure criterion and the Hoek-Brown failure criterion using the test results. The characteristics of both failure criterions were investigated through comparing the estimated rock strength parameters. As the result of the Mohr-Coulomb criterion, the cohesions and the internal friction angles are determined as 5.35 MPa and $50.25^{circ}$ of Pyoseonri basalt, 16.99 MPa and $60.66^{circ}$ of Trachy-basalt, and 2.33 MPa and $37.05^{circ}$ of Scoria, respectively. The cohesions and internal friction angles were estimated by the Hoek-Brown failure criterion in the basis of the results of regression analysis. The cohesions and the internal friction angles are determined as 4.77 MPa and $52.47^{circ}$ of Pyoseonri basalt, 14.69 MPa and $60.70^{circ}$ of Trachy-basalt, and 2.22 MPa and $47.60^{circ}$ of Scoria, respectively. As the result of comparison between the Mohr-Coulomb failure criterion and the failure envelope predicted by the Hoek-Brown criterion, the cohesion estimated by the Hoek-Brown criterion is usually lower than that obtained from the Mohr-Coulomb criterion, whereas the friction angle estimated by the Hoek-Brown criterion is higher than that obtained from the Mohr-Coulomb criterion.