This paper presents a study of the influence of basalt rocks' phase composition, acidity modulus, and structural parameter NBO/T on the tensile strength and elastic modulus of basalt continuous fibers (BCFs) derived from them. A series of BCF samples based on 14 different basalt deposits was obtained under equal conditions. The tensile strength and elastic modulus of the BCFs from different deposits vary in the ranges of 1495-3380 MPa and 58.2-78.7 GPa, respectively. Using the original method of quantitative phase analysis based on the Rietveld method, the phase compositions of the 14 deposits were defined. All deposits can be used to obtain BCFs. In the studied natural rocks, the main component is tectosilicates; the mass content of framework aluminosilicates is in the range of 16.5-3.3 mass percent. The second main component is inosilicates; the mass content of chain aluminosilicates is in the range of 6.0-58.0 mass percent. The correlations among phase composition, acidity modulus, ratio of non-bridging oxygens to tetrahedral cations, tensile strength, and elastic modulus of the BCFs from the 14 different basalt deposits were calculated. There were strong positive correlation between tectosilicate minerals mass content and elastic modulus [Pearson correlation coefficient (PCC) of 0.7] and strong negative correlation between content of chain and layered aluminosilicates and elastic modulus (PCC of - 0.74).