Abstract: New solutions are obtained for Novozhilov's equation of toreidal shells having general slenderness ratio 0<a<1(a=a/R). In contrast to the results by continued fractiontechnique, the exponents and expansion coefficients of our series solutions are all closed and explicit. The series satisfies shell equation identically. Convergence proof is also demonstrated.Explicit expressions for boundary effect and monodromy indices are also given. Finally, we discuss the possibility of applying the present method to solve the fundamental system of equations for elastic shells with rotational symmetry.