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A model for numerical simulations of intracavity-pumped quasi-three-level lasers has been developed. The model considers upconversion losses and ground-state depletion, as well as the spatial distribution of the diode pump beam. It has been applied to a Ho:YAG laser intracavity pumped by a Tm:YLF laser. A wavelength shift of the Tm:YLF pump laser, as well as dual wavelength operation, will be discussed. The laser system has been optimized with respect to the reflectivity of the output mirror and the crystal length or dopant concentration of the Ho:YAG crystal. The lasing performance of the intracavity system will be compared to an optimized Tm:YLF-Ho:YAG laser system with separated cavities. We found that the ratio of the spot sizes in the YLF and YAG crystal has strong influence on the performance of the intracavity configuration. Simulations of a Ho:YAG laser intracavity pumped by a diode-pumped Tm: YAG laser show good agreement with experimental results taken from the literature.