A critical speed analysis of a pump shaft has been investigated. Among various methods in the shaft critical speed calculation, a transfer matrix method has been examined in this research. After a brief review on the transfer matrix method, a modeling procedure for a continuous structure has been discussed. Then, a critical speed of a multistage pump shaft has been estimated up to several low modes. Throughout an analysis, parametric effects on the bearing stiffness, a degree of the modeling order, and attachmant of the impeller have been investigated. As an application example, a critical speed analysis of a verical pump which has been implemented in domestic electric power plants for cooling water circulation has been conducted in order to provide a safe operation as far as a pump vibration is concerned.