Transfer line is a serial arrangement of machines where buffers are used to separate two consecutive machines. This special type of production systems have high production volumes. In the design and operation of transfer lines, throughput analysis is essential. Considering the transient state of the systems, this paper presents theoretical analysis for throughput rate of transfer lines. For the short transfer lines, having a unique machine and two machines, we derive throughput rate, expected value and variance functions. We use these functions in performance evaluation of production systems. Besides, these theoretical analyses can be used while analyzing longer and more complex transfer lines which can easily be decomposed into smaller sub-systems.