An analytical three-dimensional (3D) coupled-wave theory (CWT) for the finite-size photonic crystal slabs (PhCs) has been presented to depict the discretized modes at band-edges residing inside and outside the continuum. Specifically, we derive the CWT equations of slow-varying envelop function of dominant Bloch waves. By combining the trial solutions that are composed of a basis of bulk states with appropriate boundary conditions (B.C.), we analytically solve the equations and discuss the far-field patterns, asymptotic behavior and flatband effect of the finite-size modes, respectively. The proposed method presents a clear picture in physics for the origins of finite-size modes and provides an efficient and comprehensive tool for designing and optimizing PhC devices such as PCSELs.