We investigate the accretion disks around compact objects with high mass accretion rates near the Eddington's critical value ME, where radiation pressure and electron scattering are dominant. This raises next problems: (a) whether stable disks could exist in relation to the theory of thermal instabilities of the disk and (b) what characteristic features the disks have if the stable disks exist. A non-rotating neutron star with the mass M = 1.4M⊙, radius R* = 107cm and the accretion rate Mac = 2.0 and 0.5Mac (models 1 and 2) is considered as the compact object. We assume the α-model for the viscosity and solve the set of two-dimensional time-dependent hydrodynamic equations coupled with radiation transport. The numerical method used is basically the same as one described by Kley and Hensler (1987) and Kley (1989) but we include some improvements in solving the difference equations (Okuda et al. 1997). The initial configuration consists of a cold, dense, and optically thick disk which is given by the standard α-model (Shakura and Sunyaev 1973) and a rarefied optically thin atmosphere around the disk.