Continuity of electricity supply with renewable distributed generation (DG) is a topical issue for distribution system planning and operation, especially due to the stochastic nature of power generation and time varying load demand. The conventional adequacy and reliability analysis methods related to bulk generation systems cannot be applied directly for the evaluation of adequacy criteria such as ‘energy supply’ and ‘continuity of service’ for distribution networks embedded with renewable DG. In this paper, new indices highlighting ‘available supply capacity’ and ‘continuity of service’ are proposed for ‘energy supply’ and ‘continuation of service’ evaluation of generation-rich distribution networks, and analytical techniques are developed for their quantification. A probability based analytical method has been developed using the joint probability of the demand and generation, and probability distributions of the proposed indices have been used to evaluate the network adequacy in energy supply and service continuation. A data clustering technique has been used to evaluate the joint probability between coincidental demand and renewable generation. Time sequential Monte Carlo simulation has been used to compare the results obtained using the proposed analytical method. A standard distribution network derived from Roy Billinton test system and a practical radial distribution network have been used to test the proposed method and demonstrate the estimation of the well-being of a system for hosting renewable DG units. It is found that renewable DG systems improve the ‘energy supply’ and ‘continuity of service’ in the distribution networks. The results suggest that the consideration of the time varying demand and stochastic renewable generation output has significant impact on the ‘energy supply’ and ‘continuity of service’ in the distribution networks.