We developed a model describing the performance of the cladding-pumped, Yb:YAG-core, fiber-like waveguide laser with a large cladding-to-core area ratio. We analyzed how pump absorption and laser output efficiencies depend on the Yb-doping level as well as the waveguide parameters, such as clad-to-core area ratio and waveguide length. We also determined the conditions that maximize both pump and laser efficiency. We showed that, depending on the waveguide design, cavity parameters as well as the core temperature, this laser can operate either at 1030 or 1050 nm. We have also shown that the main factor limiting power scaling of such a waveguide laser is the core temperature. The model was validated by laser experiments with a 174 mm long, double-clad, Yb(20%):YAG-core waveguide, with the cladding-to-core area ratio of 43.4. An output power of 41.6 W and slope efficiency of 73% with respect to the absorbed pump power have been achieved with cladding pumping by a fiber-coupled laser diode module at 933 nm. Our experimental results were in a good agreement with the modeling predictions.