Although mechanical properties of concrete under uniaxial compression are important to design concrete structure, current design codes or other empirical equations have clear limitation on the prediction of mechanical properties. Various types of fiber-reinforced reactive powder concrete matrix were tested for making more usable and accurate estimation equations for mechanical properties for ultra high strength concrete. Investigated matrix has compressive strength ranged from 30 MPa to 200 MPa. Ultra high strength concrete was made by means of reactive powder concrete. Preventing brittle failure of this type of matrix, steel fibers were used. The volume fraction of steel fiber ranged from 0 to 2%. From the test results, steel fibers significantly increase the ductility, strength and stiffness of ultra high strength matrix. They are quantified with previously conducted researches about material properties of concrete under uniaxial loading. Applicability of estimation equations for mechanical properties of concrete was evaluated with test results of this study. From the evaluation, regression analysis was carried out, and new estimation equations were proposed. And these proposed equations were applied into stress-strain relation which was developed by previous research. Ascending part, which was affected by proposed equations of this study directly, well fitted into experimental results.