The viability of a telemedicine system is the strength of its business continuity. Business continuity can only stand if the telemedicine system remains continuously feasible. This article studies telemedicine risk in terms of its feasibility on all its five components: economical, technical, social, operational, and legal/ethical. Any deficiencies in one or more of the feasibility components will affect the system business continuity risk and can lead to infeasibility and possible dissolution. The telemedicine computing environment is full of uncertainties and ambiguities and it just involves too much background knowledge that Bayesian theory cannot accommodate. Decision theory however offers a basic evidence-based multi-criteria decision mechanism that can tackle those decision problems treating both quantitative and qualitative criteria under various uncertainties including ignorance and randomness. We propose an evidential reasoning model to assess a telemedicine business continuity risk based on infeasibility. This business continuity risk is modelled using Dempster and Shafer Theory as the plausibility of infeasibility of the telemedicine system. A numerical example is provided to demonstrate the working of the proposed risk assessment model.