A production system is characterized by both its steady state and transient properties. While extensive research efforts have been spent in the analysis of the steady state of production systems, very few results, especially analytical ones, have been reported regarding their transient behavior. Indeed, transient behavior of production systems has significant practical and theoretical implications. A better understanding of the transient properties of production systems is critical to effective utilization of real-time production data for efficient factory floor operation and management. In the framework of serial production lines with geometric machines and finite buffers, this paper develops mathematical models for transient analysis and derives closed-form expressions for evaluating the production rate, consumption rate, work-in-process, and probabilities of machine starvation and blockage, during transients. In addition, a computationally efficient algorithm based on aggregation is developed to approximate the transient performance measures with high accuracy. Numerical experiments show that the methods developed can be applied to systems with time-varying machine parameters as well.