Electrodes erosion caused by spark discharge can lead to effective nanoparticles formation. In this work, we present the simulation of the early stage of the discharge formation. In particular, streamer parameters are calculated in 1D and in 2D and compared with the results of previous experiments and models [1-3]. Two infinite parallel-plate electrodes are considered, the initial electron distribution is Gaussian at the anode. Electron's drift and diffusion, Townsend ionization and photo-ionization processes are shown to be dominant factors of positive streamer formation and propagation. An implicit scheme is applied for the calculation of the electric field based on Poisson's equation. The calculation results demonstrate a transition from streamer to spark. In addition, we calculate the power input for the following cathode erosion thus providing initial conditions for nanoparticle formation model (next step). This work is performed in the frame of the FP7 project "BEOUNAPART-E". The results of the model are under verification by a comparison with the experimental results obtained by other partners. [1]. N. S. Tabrizi, Q. Xu, N. M. van der Pers and A. Schmidt-Ott, Generation of mixed metallic nanoparticles from immiscible metals by spark discharge, J. of Nanopart. Research 12, 1 (2010), 247-259. [2]. A A Kulikovsky, Two-dimensional simulation of the positive streamer in N2 between parallel-plate electrodes, J. Phys. D: Appl. Phys. 28 (1995) 2483-2493. [3]. A Bourdon, V. P. Pasko, N. Y. Liu, S C'elestin, P. S'egur and E. Marode, Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations, Plasma Sources Sci. Technol. 16 (2007) 656-678.