Volume visualization is a very active research area in the field of scien-tific visualization. The Extreme Vertices Model (EVM) has proven to be a complete intermediate model to visualize and manipulate volume data using a surface rendering approach. However, the ability to integrate the advantages of surface rendering approach with the superiority in visual exploration of the volume rendering would actually produce a very complete visualization and edition system for volume data. Therefore, we decided to define an enhanced EVM-based model which incorporates the volumetric information required to achieved a nearly direct volume visualization technique. Thus, VolumeEVM was designed maintaining the same EVM-based data structure plus a sorted list of density values corresponding to the EVM-based VoIs interior voxels. A function which relates interior voxels of the EVM with the set of densities was mandatory to be defined. This report presents the definition of this new surface/volume integrated model based on the well known EVM encoding and propose implementations of the main software-based direct volume rendering techniques through the proposed model.