Cold spray is a rapidly developing coating technology for depositing materials in the solid state. In this deposition process, the spray particles are accelerated to a high velocity by a high-speed gas flow, and then form a dense and high quality coating due to plastic deformation of particles impinged upon the solid surface of substrate. 2D and 3D modelling of particle impacting behaviours in cold spray deposition process by using ABAQUS/Explicit was conducted for four couples of materials (i.e. impacting particle/impacted substrate): copper/aluminium, aluminium/copper, copper/copper, and aluminium/aluminium. A systematic analysis of a single impact was carried out considering different parameters, such as the initial impact velocity, initial temperature and contact angle, which affect the deposition process and subsequently the mechanical properties of coating. Three numerical methods have been evaluated and their performances are discussed for various simulation settings: (i) modelling in a Lagrangian reference frame; (ii) modelling using adaptive remeshing in an Arbitrary Lagrangian Eulerian (ALE) reference frame; and (iii), modelling in a CEL reference frame. It is found that the Coupled Eulerian Lagrangian (CEL) method has more advantages to simulate the large deformation of materials, and is also more efficient to prevent the excessive distortion of the mesh. A comparison between simulation results and experimental data from the literature was performed. Nevertheless, the CEL method is implicitly isothermal for ABAQUS v6.10, whereas the modelling in the classical Lagrangian reference frame does include coupled thermo-mechanical effects with a local increase of the temperature near the interface - due to friction - and for the highly plastically deformed elements - due to the heat dissipation linked to plasticity. A local rise of temperature at the impact surface may also be observed for oblique impacts. Finally a first attempt to simulate the deposition of several particles is made with a 3D CEL model, resulting in the creation of porosity at the interface between particles.