To　investigate　the　gain　characteristics　of　optically　pumped　vertical　external　cavity　surface　emitting　lasers,　taking　InGaAs/GaAs　strained　quantum　wells　as　an　example,　a　complete　system　model　which　considers　all　the　effects　of　the　band-gap,　band-edge　discontinuities　and　band　structure　is　established.　In　view　of　the　valence　band　mixing　and　the　wave　function　mixing,　the　6×6　effective-mass　Luttinger-Kohn　Hamiltonian　is　solved　by　using　the　finite　difference　method,　and　the　conduction-band　structures,　the　valence-band　structures　and　envelope　functions　are　obtained.　And　then　the　material　gain　and　spontaneous　radiation　spectrum　with　linear　Lorentzian　function　are　simulated　numerically.　Finally,　the　effects　of　the　well　width,　carrier　density,　temperature　and　other　factors　on　the　quantum-well　gain　are　discussed.　The　calculated　results　provide　a　theoretical　basis　for　the　optimized　design　of　optically　pumped　vertical　external　cavity　surface　emitting　lasers.