Experimental studies on gain and saturation of a Yb-doped double-cladding fiber amplifier accompanied with and interpreted by rigorous numerical simulations are presented. The saturation power, the value, and the spectral asymmetry of the output signal are experimentally characterized in both pulsed and continuous wave (CW) operation, and then, verified and interpreted numerically. Power conversion efficiency and quantum conversion efficiency of the amplifier are measured to be up to 55% and 58%, respectively. It is the first time, to the best of our knowledge, to demonstrate a numerical model for the pulsed operation based on the interaction of vector coupled nonlinear Schrodinger equations and the rate equations of the Yb-doped double-clad fiber taking into account all high-order dispersion parameters and the variation of gain coefficient during pulse propagation. A good agreement between numerical and experimental results is observed providing interpretations to the results. The numerical models and the experimental demonstrations provide guidance for the design and analysis of Yb-doped double-cladding fiber amplifiers both in pulsed and CW operation.