In this paper we investigate the limit behavior of the solution to quasi-static Biot equations in thin poroelastic flexural shells as the thickness of the shell tends to zero and extend the results obtained for the poroelastic plate by Marciniak-Czochra and Mikelic in [Arch. Ration. Mech. Anal., 215 (2015), pp. 1035--1062]. We choose Terzaghi's time corresponding to the shell thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure, and total poroelastic stress to the solution of the new class of shell equations. The derived bending equation is coupled with the pressure equation, and it contains the bending moment due to the variation in pore pressure across the shell thickness. The effective pressure equation is parabolic only in the normal direction. As an additional term it contains the time derivative of the middle-surface flexural strain. Derivation of the model presents an extension of the results on the derivation of classical linear elastic shells by ...