In this paper, we first formulate a linear quasi-static poroelastic shell model of Naghdi's type. The model is given in three unknowns: displacement Q u of the middle surface, infinitesimal rotation Q ! of the cross section of the shell, and the pressure . The model has the structure of the quasi-static Biot's system and can be seen as a system of the shell equation with pressure term as forcing and the parabolic type equation for the pressure with divergence of the filtration velocity as forcing term. On the basis of the ideas of the operator splitting methods, we formulate two sequences of approximate solutions, corresponding to 'undrained split' and 'fixed stress split' methods. We show that these sequences converge to the solution of the poroelastic shell model. Therefore, the iterations constitute two numerical methods for the model. Moreover, both methods are optimized in a certain sense producing schemes with smallest contraction coefficient and thus faster convergence rates. Also, these convergences imply existence of solutions for the model. shell model; undrained and fixed stress split; iterative numerical method; existence of solutions 1) formulate a linear quasi-static model of poroelastic shells (of Naghdi type), 2) formulate two iterative sequences of solutions of the problems associated to the formulated poroelastic shell model (one of the sequences is related to the 'undrained split' iterative method and the other to the 'fixed stress split' iterative method, which are usually applied in geomechanics), 3) prove the convergence of these sequences to the solution of the formulated poroelastic shell model.The proposed model is closely related to the poroelastic shell models derived asymptotically from the three-dimensional Biot's equations in [2,3].There are many different shell theories that can be found in the literature. Within the classical elasticity, we mention the membrane shell model, the flexural shell model, the generalized membrane shell model, the Koiter model (see references [4][5][6][7] or [8]), the Naghdi shell model (see references [9,10]) and the newly introduced models of the Koiter and Naghdi type (see references [11,12], a very similar model already appears in [13]), which are well defined for Lipschitz middle surfaces. All these models are two-dimensional models (defined on a two-dimensional domain) and describe behavior of three-dimensional elastic bodies that are thin in one direction.In geomechanics, there are many examples of elastic bodies which are saturated by a fluid, see e.g., references [14,15]. Their overall behavior can be modeled by the quasi-static Biot's system of partial differential equations, see reference [1] or [16]. It couples the equations of linearized elasticity, containing the pressure gradient of the flow, with the mass conservation equation involving the fluid