Composite lattice shells are highly efficient and extensively used in various structural applications, such as rocket interstages, payload adapters for spacecraft launchers, fuselage components for aerial vehicles, and components of the deployable space antennas. The aim of this paper is to present an analytical approach based on the finite element discrete modelling that is capable of predicting mechanical behaviour of composite lattice structures with sufficient accuracy and, at the same time, is affordable in terms of computational expenses. This allows the modelling approach proposed in this work to enable the efficient solution of relevant design and design optimisation problems. Structural analyses reported in the literature have been conventionally performed for composite cylindrical lattice shells. The paper investigates buckling behaviour of anisogrid composite lattice cylindrical, conical, and parabolic shells. The lattice shells are modelled as three-dimensional frame structures composed of curvilinear ribs subjected to the tension/compression, bending in two planes and torsion. The specialised finite-element model generation procedure (model generator/design modeller) is developed to control the orientation of the beam elements allowing the original twisted geometry of the curvilinear ribs to be closely approximated. The generation of discrete models are presented and explained in detail for cylindrical and conical lattice shells. Buckling analyses are performed for the cylindrical and conical shells subjected to axial compressive loading, and for the structure composed of parabolic lattice shell loaded by transverse concentrated external load. The effects of varying the length of the shells, the number of helical ribs and the angles of their orientation on the buckling behaviour of lattice structures are investigated. Critical buckling loads and corresponding buckling mode shapes are determined based on the modelling approach proposed in this work. The effects of parameters of the lattice structure on the values of critical buckling loads, mode shapes are examined using parametric analyses. Based on the computations, the angles of orientation of helical ribs delivering maximum critical loads for a number of particular structural designs are identified. The results of these studies indicate that the modelling approach presented in this work can be successfully applied to the solution of design problems formulated for composite lattice shells.