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Energy consumption and resource utilization in a data center is an issue that preoccupies small and large business managers.Studies were well conducted to answer the problem.The technology such as cloud computing,the virtualization offers solutions to reduce the considerable rate of energy consumed by the physical machine running and where misuse resources utilization.The physical machine is considered the component that consumes the most energy compared to other components(air conditioning,lighting,so on).This study will take consideration the energy consumed by the physical machine(or server)component.The packing of the virtual machine to the physical machine is formulated,2-dimensional bin packing problem with only two constraints(CPU and Memory).In this dissertation,the algorithm(the Particle Swarm Optimization)for the virtual machine placement problem is implemented to find:(1)a best position for each virtual machine;(2)minimize the number of physical used and(3)to reduce the energy consumed by the server.Experimental results show that the algorithm(the PSO)performs effectively in every situation,when tacking a small size of sample and scales up well when the number of samples increases.To search a better solution to the problem we apply an optimization method and evaluation the minimization problem to virtual machine placement in cloud data center.1)This dissertation presents an approach to solve Virtual Machine Placement,for that 2-dimensional mathematical model for bin packing problems is formulated,this assign be renting the Virtual machine to the smallest number of physical machine,to minimize the energy used and to balance the load of each bin.2)The proposed algorithm optimizes the energy cost by placing the virtual machine to smallest number of server.3)The evaluation tests result of the algorithm will be compare to other approach First-fit and finding that the algorithm performs better than First-fit.