After the introduction of technical background and unique merits of a diode-pumped alkali laser (DPAL), the present research conditions are described in development of master oscillator power-amplifier (MOPA) for DPALs. The systematic calculation is carried out after construction of a rate-equation model of an end-pumped DPAL-MOPA system using the three-level stimulated absorption-stimulated emission theory of an alkali atom. The output power and extraction efficiency are analyzed when the temperature, cell length, pump power, and waist radius are varied, respectively. Compared with the experimental data, the calculated results are in coincident with them, which demonstrates the developed model is effective. The research is thought to be useful in realization of the power scaling of a DPAL system.