In the present study a two-mode, separately concurring resonant cavity model is proposed for theoretical interpretation of the 3 minute umbral oscillation. The proposed model has been investigated by calculating the transmission coefficients of the waves propagating through the umbral photosphere (photospheric weak-field cavity) and chromosphere (chromospheric strong-field cavity) into the corona, for 3 different umbral model atmospheres by Staude (1982), Beebe et al. (1982) and Avrett (1981). In computing the transmission coefficients we made use of multi-layer approximation by representing the umbra] atmosphere by a number of separate layers with (1) temperature varying linearly with depth and (2) temperature constant within each layer. The medium is assumed to be compressible, non-viscous, perfectly conducting under gravity. The computed resonant periods, transmission spectra, phase spectra, and kinetic energy density of the waves associated with the oscillations are presented in comparison with the observations and their model dependent characteristics are discussed.