Due to linear accelerators restrictions and followed the invention of lasers from the state Pettaw ( ), nuclear accelerators (based on laser-plasma interaction) are highly regarded in the past decade. In this type of accelerators, first high-power laser pulse impacts with target, the part of target that is irradiated by laser, is quickly ionized and becomes the plasma. Because of the charge separation, strong electrical field of the order is created in plasma that is the basis of the acceleration of particles in accelerators of this type. Electrons and ions accelerated in nuclear accelerators are used in different applications such as fast ignition fusion and medical aplications. In the past decade production and acceleration of ions using radiation of high-power laser to the laminar target, has been highly considered. Published ion beams, especially protons, contain a large number of particles ( ) with energies of MeV. With the arrival of the laser pulse into the plasma, electrons oscillate under the influence of the incoming wave electrical field and ions due to the inertia opportunity do not respond to these fluctuations. Therefore the separation of charges between ions and electrons leads to the creation of a disturbed electrical field that oscillates with frequency equal to the initial wave frequency. Beat between the electrical field of the initial wave and the disturbed electric field caused by the separation of charges causes pondermotive force. Pondermotive force leads to local changes in the intensity of the electron plasma. This, changes the optical properties of the plasma in areas where the laser pulse exists. Followed by, changes laser pulse propagation and eventually the laser pulse shape. Created perturbations in the initial laser pulse lead to the creation of the filamentation instability. This instability causes the beam to break the strings. In this thesis, we have used two-dimensional particle-in-cell simulation code (XOOPIC) simulated femtosecond laser pulse interaction with the solid target copper. we radiated laser pulse with an intensity once to the copper sheet and once again to aluminum sheet with a thickness of 515 nm and investigated string growth of accelerated particles beam. By running the simulation program we observed which filamentation instability leads to string of beam of particles generated in copper and also in aluminum and thus reduces the intensity of the produced beam, but string growth in the aluminum sheet is more than string growth in the copper sheet.