This paper studies the optimization problem of distributing traffic load onto multiple engines in parallel packet forwarding systems. Given that the power dissipation of each engine can be formulated as a function of traffic load going through that engine, we develop a theoretical framework to minimize the overall power consumption while satisfying the throughput demand. We consider two types of power functions, which are different in terms of whether supporting sleep mode or not. Accordingly, the two power functions lead to two different mathematical programming problems: one can be solved via linear programming (LP), the other is modeled as non-linear programming and can be solved via mixed integer programming (MIP). Our simulation using a 18-hour real-life traffic trace shows that our solution can achieve significant power/ energy reduction compared with the traditional parallel forwarding scheme based on load balancing. We also discuss the system design issues and identify the challenges for real implementation. We believe our optimization framework and algorithmic solutions are applicable for load distribution in other parallel systems e.g. data centers and clusters.