An energy shell structure depending on eccentricity is analyzed in a dielectric elliptic microcavity. Through the analysis, it is explicated that the energy shell structure is governed by classical constant actions of periodic orbits. For clarification, the relation between dominances of the periodic orbits and bifurcation behaviors are obtained and the length spectra based on eigenvalues computed by a numerical method are compared with the exact lengths of the periodic orbits obtained by analytic calculations. By matching effective wave numbers obtained from the periodic orbit lengths to exact wave numbers of stationary states in closed and open cavities, we find deviations provoked from the openness. We show that these deviations are caused by additional phase factors in the Einstein-Brillouin-Keller quantization.