In　many　applications,　particularly　in　the　econometric　area　and　industrial　quality　improvement　experiments,　there　is　a　great　need　to　model　the　variance.　A　unified　procedure　was　proposed　to　simultaneously　select　significant　variables　in　joint　mean　and　variance　models　which　provide　a　useful　extension　of　the　classical　normal　regression　models.　It　is　further　shown　that　the　presented　penalized　estimator　enjoys　the　consistency　and　the　oracle　property.　Simulation　and　practice　show　that　this　model　and　method　are　useful　and　effective.