This work deals with the application of meshless local integral equations (LIEs) based on meshless local Petrov-Galerkin (MLPG) method to two dimensional coupled non-Fick diffusion-thermoelasticity analysis, in which the energy equation is based on Green – Naghdi theory of generalized coupled thermoelasticity. A unit step function is used as the test functions in the local weak-form. It leads to local integral equations (LIEs). The analyzed domain is divided into small subdomains with a circular shape. The radial basis functions are used for approximation of the spatial variation of field variables. For treatment of time variations, the Laplace-transform technique is utilized. The molar concentration diffuses through 2D domain with a finite speed similar to thermoelastic waves. The propagation of mass diffusion, temperature and elastic waves are obtained and discussed at various time instants. The MLPG method has a high capability to track the diffusion, elastic and thermal wave fronts at arbitrary time instants in 2D domain. The profiles of molar concentration, temperature and displacements in two orthogonal directions are illustrated at various time instants.

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