The latest developments in mobile computing technology have increased the computing capabilities of smart mobile devices (SMDs). However, SMDs are still constrained by low bandwidth, processing potential, storage capacity, and battery lifetime. To overcome these problems, the rich resources and powerful computational cloud is tapped for enabling intensive applications on SMDs. In Mobile Cloud Computing (MCC), application processing services of computational clouds are leveraged for alleviating resource limitations in SMDs. The particular deficiency of distributed architecture and runtime partitioning of the elastic mobile application are the challenging aspects of current offloading models. To address these issues of traditional models for computational offloading in MCC, this paper proposes a novel distributed and elastic applications processing (DEAP) model for intensive applications in MCC. We present an analytical model to evaluate the proposed DEAP model, and test a prototype application in the real MCC environment to demonstrate the usefulness of DEAP model. Computational offloading using the DEAP model minimizes resources utilization on SMD in the distributed processing of intensive mobile applications. Evaluation indicates a reduction of 74.6% in the overhead of runtime application partitioning and a 66.6% reduction in the CPU utilization for the execution of the application on SMD.