Different methods have been considered for using nuclear energy in recent years. The main goal of these methods is to access high energy gain. In the conventional methods of inertial confinement fusion hydrodynamic instability in the compression process reduce energy gain. The methods for reducing instabilities imply the compression of fuel by laser or ion beams in two phases. First phase, preheating the fuel by laser or ion beams and then producing the relativistic electrons by laser pulses with power of within the fuel that is done in the second phase. This method of heating fuel has been proposed as a fast ignition method. In this thesis, fast ignition is investigated in cylindrical chamber. Fast ignition and cylindrical chamber to one-step ignition guaranty high energy gain and conventional method can alternate with it. In orther to determine the energy gain of inertial confinement fusion in multi- layer balls it is necessary to solve the equatio which are related to the behavior of the plasma in confinement time. Multi-layer balls in the central region of fuel is compressed by energetic laser or heavy ion beams. Appropriate choice of the mass ratio of fuel layers to jogger layer lead to ignition of central region. In the case which the ball reaches maximum density, fuel density reaches the density more than 500 to 1000 times of solid fuel density. In the area of cold fuel temperature rises rapidly then the plasma is formed and the fusion interactions start. Calculating the density variation, temperature and pressure in plasma is necessary for determining the kinetic energy flux of neutrons and electrons and the radiation that comes out of the ball. By using the numerical solution of continuity, force and energy equations, MHDFCT program is provided for determining the energy, velocity, temperature and pressure (after compression). Keywords: Fusion, Inertial, (ICF), Hydrodynamic, Ignition, Plasma.