It is possible to count and perform quench correction on two ${beta}$ -label samples so long as the maximum ${beta}$-energies are sufficiently different. However, when 4he conventional technique is applied to the radioassay of a mixture of more than three nuclides, the reliability of the activities determined is considerably reduced, resulting from the large overlapping of liquid scintillation pulse height distributions of each nuclide. A technique that allows the activities of multiple ${beta}$-labeled samples to be radioassayed was proposed by using the least square method. The technique was applied to mixture samples of $^3H,;^{14}C,;^{36}Cl$, and $^{90}Sr$. The analytical values were in good agreement with the reference values within 7% relative error.