The present paper is devoted to the formulation of the theory of laminated anisotropic shells. Firstly, a unified representation of displacement variation across the thickness of arbitrary shaped laminated shells is derived on the basis of rigorous kinematical analysis, and then a Karman-type non-linear theoyr of such shells is established after taking some approximations for the displacement variation. The theory satisfies the continuity conditions of displacements and tractions at layer interfaces as well as the external boundary conditions on the bounding surfaces, and the governing equations contain only five independent variables. In order to assess the accuracy of the theory, numerical results for some special cases are illustrated and compared with the corresponding exact solutions of three-dimensional elasticity.NOTATIONV space occupied by the shellV ( m ) space occupied by the mth layer, for m = 1 kΩ ( 0 ) bottom surface of the shellΩ ( k ) top surface of the shellΩ ( m ) interface between the mth and (m + 1)th layers, for m = 1, 2 k - 1A lateral surface of the shellh total thickness of the shellθ 3 ( m ) distance between Ω ( m ) and Ω ( 0 ) , for m = 0, 1 kR = R(θ 1 , θ 2 ) position vector of a point (θ 1 , θ 2 ) on Ω ( 0 ) r = r(θ 1 , θ 2 , θ 3 ) position vector of a point (θ 1 , θ 2 , θ 3 ) in Va α covariant base vector, given by a α = R , α g i covariant base vector, given by g i = r , i δ β α mixed Kronecker delta α β covariant components of the two-dimensional permutation tensorμ β α mixed components of the shifter tensorb β α mixed components of the curvature tensorμ determinant of the shifter tensor