We propose an accurate and efficient estimation method of transverse shear stresses for analysis and design of laminated composite structures by 4-node quadrilateral degenerated shell elements. To get proper distributions of transverse shear stresses in each layer, we use 3-dimensional equilibrium equations instead of constitutive equations with shear correction factors which vary diversely according to the shapes of shell sections. Three dimensional equilibrium equations are integrated through the thickness direction with complete polynomial membrane stress fields, which are recovered by REP (Recovery by Equilibrium in Patches) recovery method. The 4-node quadrilateral degenerated shell element used in this paper has drilling degrees of freedom and shear stresses derived from assumed strain fields that are set up at natural coordinate systems. The numerical results demonstrate that the proposed estimation method attains reasonable accuracy and efficiency compared with other methods and FE analysis using 4-node degenerated shell elements.