ABSTRACT Continuum kinematics-inspired peridynamics (CPD) is a peridynamic (PD) formulation that uses the same kinematic measures as classical continuum mechanics (CCM), providing a geometrically exact formulation [1]. PD is a non-local continuum formulation, wherein the behaviour of each material point is influenced by material points within a finite neighbourhood of that point [2]. By incorporating non-locality as a fundamental modelling concept, the range of interactions considered at each point is expanded, encompassing influences beyond its immediate neighbours. Simultaneously, the integral formulation eliminates the need for explicit spatial gradient computations, making it highly suitable for modelling complex heterogeneous materials. This contribution focuses on the implementation of transverse isotropy within the CPD framework [3]. Transverse isotropic materials exhibit distinct properties in a specified direction. Capturing anisotropy in constitutive models is important to gain insight into the interrelation of structural components and the mechanical response of materials like biological tissue [4]. The CPD framework employs rational mechanics to effectively model transverse isotropy at finite deformation while preserving the fundamental deformation measures of length, area and volume intrinsic to classical continuum mechanics. This is achieved by describing the transverse isotropy through invariants that depend on the transformation of finite line and area elements, i.e., the secant maps and the preferred fibre direction. Furthermore, the framework’s versatility is highlighted by representing transverse isotropy through the deformation of finite area elements to accommodate materials with varying Poisson’s effect. A novel transverse isotropic constitutive model for finite elastic deformations within the CPD framework is proposed. The constitutive model satisfies material objectivity, is inherently stable and enhances modelling flexibility through area-element-based transverse anisotropy, offering a powerful tool for simulating complex material behaviour. REFERENCES [1] A. Javili, A. McBride, P. Steinmann, Continuum-kinematics-inspired peridynamics. Mechanical problems, J. Mech. Phys. Solids 131 (2019), pp. 125–146. [2] Silling, S. A. (2000). Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces. Journal of Mechanics and Physics of Solids. [3] A.M. De Villiers, J. Stadler, G. Limbert, A.T. McBride, A. Javili, and P.