The paper is devoted to consideration of methodological, large-scale data management, medical imaging and software developing issues concerned with the distributed computing in a national-wide telemedicine system. The system substantially exploits the image data provided with the complementary pulmonary X-ray and chest computed tomography (CT) image modalities; its aim is to provide the computerized support of lung disease diagnosis. The computational environment is heterogeneous and is based on PCs and dedicated servers located in medical institutions, as well as on the supercomputer installed in the National Supercomputer Center of Belarus. For utilizing the grid infrastructure, the distributed computing architecture employs the Unicore as a middleware, as well as the Message Passing Interface. At present the project is on its early stage. However, the preliminary research and experimentation performed in framework of the project already involves X-ray lung image data of more than 100 thousands of patients and about a hundred of 3D CT scans of the lungs accumulated in the database.