We present the results of a novel numerical and experimental investigation aimed at obtaining efficient $1.05\mathrm{\mu m}$ operation with a Yb:YAG laser. The model shows that the emitting wavelength of the Yb:YAG laser is affected by the combination of length and doping concentration of the gain medium. Efficient continuous-wave laser operation at the wavelength of $1050\mathrm{nm}$ was experimentally obtained in good agreement with the model predictions. Based on continuous-wave operation, generation of $1.8\mathrm{ps}$ laser pulses at the central wavelength of $1050\mathrm{nm}$ , as well as $170\mathrm{fs}$ laser pulses at the central wavelength of $1053\mathrm{nm}$ , were realized.