A boundary element method (BEM) based on multiple reciprocity method(MRM) is employed to solve eigenvalue and eigenfrequency of a two-dimensional linear acoustic cavity.By direct searching of the zero-points of determination of a matrix,we determine eigenfrequency of the system.An effective estimation for the first wave-number was suggested based on the principle of wave propagation.Estimation efficiency of several models is calculated.We evaluated fundamental solution's order and found that more than seven reciprocity are needed.Numerical results agree well with analysis and other literature.Estimation for the first wave-number is effective and correct.