A parallel geomechanics model for describing naturally fractured rock deformation is developed and tightly coupled with a dual porosity/dual permeability black oil model. The geomechanics model is developed with capabilities of modeling both rock matrix and the fracture deformations, as well as their effects on reservoir properties. An advanced constitutive law with the fracture deformation mechanism is proposed. The multiphase flow model is modified by introducing geomechanical variables. The matrix porosity and fracture permeability are chosen as coupling parameters between geomechanics and fluid flow models. An iteratively coupling method is employed in order to fully capture interactions between solid and flow. Moreover, parallel computing is employed to handle large scale problems by benefiting from its features of distributed memory storage and efficient runtime reduction. Geomechanical effects on the reservoir pressure distribution are illustrated by a numerical experiment. In addition, for testing the scalability behavior, a large scale problem with millions of grid blocks is performed on multiple processors. The result shows an encouraging speedup which indicates the integrated model can be an efficient and useful tool for predicting and analyzing oil/gas production of naturally fractured reservoirs.