###### Abstract  
This work investigates the mechanical behaviour of sandwich beams with cellular cores using a multiscale approach combined with a meshless method, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The analysis is divided into two steps, aiming to analyse the efficiency of NNRPIM formulation when combined with homogenisation techniques for a multiscale computational framework of large-scale sandwich beam problems. In the first step, the cellular core material undergoes a controlled modification process in which circular holes are introduced into bulk polyurethane foam (PUF) to create materials with varying volume fractions. Subsequently, a homogenisation technique is combined with NNRPIM to determine the homogenised mechanical properties of these PUF materials with different porosities. In this step, NNRPIM solutions are compared with high-order FEM simulations. While the results demonstrate that RPIM can approximate high-order FEM solutions, it is observed that the computational cost increases significantly when aiming for comparable smoothness in the approximations. The second step applies the homogenised mechanical properties obtained in the first step to analyse large-scale sandwich beam problems with both homogeneous and functionally graded cores. The results reveal the capability of NNRPIM to closely replicate the solutions obtained from FEM analyses. Furthermore, an analysis of stress distributions along the beam thickness highlights a tendency for some NNRPIM formulations to yield slightly lower stress values near the domain boundaries. However, convergence towards agreement among different formulations is observed with mesh refinement. The findings of this study show that NNRPIM can be used as an alternative numerical method to FEM for analysing sandwich structures. the development of efficient and accurate numerical methods for predicting the structural response of sandwich structures remains an ongoing challenge. The most common approach for analysing sandwich panels and laminates involves equivalent single-layer (ESL) theories [3]. These theories employ a 2D discretisation and model the laminate thickness using a transverse deformation theory. When compared to a full 3D deformation elasticity theory applied to 3D discretisations, this dimensional simplification offers a significant reduction in computational cost. However, 3D solutions provide a more realistic representation of physical phenomena and offer more accurate predictions than 2D ESL theories, particularly when dealing with thick plates and shells [4]. Various analytical approaches employing 3D elasticity theory have been proposed to explore the bending behaviour of sandwich plates. In the seminal research by [PERSON] [5], exact 3D solutions were formulated for stress analysis of simply supported rectangular sandwich plates. Subsequently, [PERSON] [6] utilised 3D elasticity equations to derive analytical bending solutions for rectangular multilayer plates subjected to distributed transverse loading. Regarding sandwich plates featuring functionally graded cores, [PERSON] and [PERSON] [7] introduced a 3D exact elasticity solution to calculate their bending response under sinusoidal distributed transverse loads. Expanding this approach, [PERSON] and [PERSON] extended the 3D exact elasticity equations to obtain the bending solution of sandwich plates under localised transverse loads [8] and various other pertinent transversal loading scenarios [9]. A detailed discretisation of the cellular material comprising the sandwich core would result in computational analysis with a significant computational cost. Consequently, to mitigate this challenge, multiscale homogenisation techniques are commonly employed to accelerate structural analyses, while yielding reasonably accurate solutions [10]. These techniques facilitate multiscale analysis by assuming the presence of multiple spatial scales within materials and structures.