The rare earth doped fiber lasers and amplifiers have attracted much attention recently in the fields of optical communication, industrial, medical and military applications. These lasers are quickly replacing conventional bulk laser devices in a variety of applications. Among their advantages we can refer to high beam quality, high efficiency, compactness and wavelength stability against the temperature variations. In these lasers it is possible to obtain kilowatts output power with more than 80% efficiency. Ytterbium doped fibers are of interest in high power applications due to their numerous advantages arising from a simple ytterbium electronic structure. However, behavior of ytterbium doped fiber devices strongly influenced by the selection of absorption and emission wavelengths, amplified spontaneous emission (ASE) and other parameters. Also increasing the power in these fibers leads to detrimental nonlinear effects. Careful theoretical analysis is required to optimize the performance of the fiber laser and amplifiers and to estimate the influence of ASE, nonlinear effects and other such phenomena. In this thesis we study the design of high power fiber laser amplifiers for amplification of continuous and nanosecond pulsed waves. In order to modeling of these amplifiers the time dependent rate equations are investigated; after derivation of these equations, we will solve them by forth order the Runge-Kutta (RK4) numerical method in the continuous wave (CW) regime and by the Finite Difference Method (FDM) in the nanosecond pulsed regime for ytterbium doped double clad (YDDC) fiber amplifiers and the amplifier behavior in this regimes are investigated. In the CW regime many characteristics such as signal, pump, ASE powers and upper state population distributions along the fiber are obtained, in the pulsed regime many characteristics such as output waveform evolution, temporal evolution of pulse energy, ASE and other things are obtained. Then ytterbium doped double clad fiber amplifiers are optimized under the forward, backward and bidirectional pumping for amplification of continuous and nanosecond pulsed waves in consideration of different parameters. Eventually a nanosecond pulsed fiber laser amplifier with output power of 100 mW, pulse width of 150 ns and pulse repetition rate of 500 kHz is fabricated and measurement results are presented. Key Words: optical fiber amplifier, Ytterbium, Double clad fiber