In this paper, the fundamentals of a mesh-free particle numerical method for electromagnetic transient simulation are presented. The smoothed particle interpolation methodology is used by considering the particles as interpolation points in which the electromagnetic field components are computed. The particles can be arbitrarily placed in the problem domain: No regular grid, nor connectivity laws among the particles, have to be initially stated. Thus, the particles can be thickened only in distinct confined areas, where the electromagnetic field rapidly varies or in those regions in which objects of complex shape have to be simulated. Maxwell's equations with the assigned boundary and initial conditions in time domain are numerically solved by means of the proposed method. Validation of the model is carried out by comparing the results with those obtained by the FDTD method for a one-dimensional (1-D) case study in order to easily show the capability of the proposed scheme