Theoretical and numerical investigations are presented for the oblique modulation of electron acoustic (EA) waves in three-component plasma consisting of cold electrons, superthermal hot electrons and stationary ions. To study the stability criteria of waves, the nonlinear Schrodinger equation (NLSE) is derived. Analytical and numerical calculations of the NLSE show the variation of the stability region with different plasma parameters. This reveals that the stability criteria of EA waves depend on the modulation angle theta. The effect of the superthermal parameter kappa and electron temperature ratio sigma on the formation of EA wave envelope excitations is also discussed.