This　paper　proposes　an　approach　to　obtain　the　steady　state　probability　density　function　(PDF)　of　nonsmooth　nonlinear　dynamical　systems　driven　by　the　Gaussian　white　noise.　The　steady　state　PDF　solution　is　assumed　to　contain　two　probability　flows　obtained　by　the　detailed　balance　method.　The　weighted　mean　squared　residuals　of　the　error　of　the　FPK　equation　are　minimized　with　respect　to　the　unknown　coefficients　in　the　assumed　solution.　The　integrability　of　the　weighted　mean　squared　residuals　is　found　to　provide　a　means　to　deal　with　the　singularities　in　the　steady　state　PDF　that　arise　from　the　nonsmooth　dynamics　of　the　nonlinear　stochastic　system.　The　accuracy　of　the　proposed　approach　is　estimated　by　the　Monte　Carlo　simulations　via　two　examples.　(C)　2018　Elsevier　B.V.　All　rights　reserved.