With rapid advancements in computer hardware, it is now possible to perform large simulations of granular flows using the Discrete Element Method (DEM). As a result, solids are increasingly treated in a discrete Lagrangian fashion in the gas-solids flow community. In this paper, the open-source MFIX-DEM software is described that can be used for simulating the gas-solids flow using an Eulerian reference frame for the continuum fluid and a Lagrangian discrete framework (Discrete Element Method) for the particles. This method is referred to as the continuum discrete method (CDM) to clearly make a distinction between the ambiguity of using a Lagrangian or Eulerian reference for either continuum or discrete formulations. This freely available CDM code for gas-solids flows can accelerate the research in computational gas-solids flows and establish a baseline that can lead to better closures for the continuum modeling (or traditionally referred to as two fluid model) of gas-solids flows. In this paper, a series of verification cases is employed which tests the different aspects of the code in a systematic fashion by exploring specific physics in gas-solids flows before exercising the fully coupled solution on simple canonical problems. It is critical to have an extensively verified code as the physics is complex with highly-nonlinear coupling, and it is difficult to ascertain the accuracy of the results without rigorous verification. These series of verification tests set the stage not only for rigorous validation studies (performed in part II of this paper) but also serve as a procedure for testing any new developments that couple continuum and discrete formulations for gas-solids flows. (c) 2011 Elsevier B.V. All rights reserved.