Rayleigh–Ritz variational method has been employed to estimate precise energy-eigenvalues of spherically compressed two-electron atoms (Z=1−10) embedded in Debye plasma with a view to modelling atom under dense plasma environment. The trial wave function is expanded in terms of explicitly correlated Hylleraas-type basis set satisfying Dirichlet's boundary condition. The combined effect of decrease in the size of spatial confinement domain and increase in Debye screening parameter pushes the system towards gradual destabilization and subsequent ionization or complete fragmentation of the system. Present results are in reasonable agreement with other results existing in literature. Within finite domain, the thermodynamic pressure experienced by the ions due to the plasma electrons is also estimated.