Business processes execution is a technologically complex procedure. In order to execute processes successfully, several aspects need to be considered. With the introduction of cloud computing the process execution migrates from the local infrastructure to the cloud. By using proposed procedure we can successfully overcome the problems related to the local infrastructure and gain the advantage of all benefits provided by the cloud computing concept. For this purpose, we introduce a novel concept of business processes mapping, which takes care of process relocation from local environment to the cloud. The proposed model is based on BPEL (Business Process Execution Language) language and transformation of its key constructs. The execution of business processes on cloud computing can be supported by mapping activities in form of workflows on the SWF (Simple Workflow Service). Mapping method of individual business process constructs depends on the complexity of the activities. Some constructs are mapped directly, while others require further decomposition and part by part mapping. Furthermore, more complex activities are mapped as composite activities or smaller workflows. Mapping performance of each activity is evaluated on a test set of business processes. The correct execution of the business process in form of SWF workflow, when compared with process execution on BPEL process server, represents an important factor for achieving successful verification. In addition to performance verification, we examined the method of implementation by sequence and number of specified activities and thus achieved an average reduction of activities by 12 %.