The Norwegian electricity distribution industry is a natural monopoly regulated by the Norwegian Water Resources and Energy Directorate (NVE). NVE decides the regulatory model which purpose is to stimulate the industry to produce at minimum cost in order to maximize consumer surplus. To be successful producing at minimal cost the individual company has to be efficient. This thesis estimates a translog cost frontier using the statistical package STATA 11.1 based on the Stochastic Frontier Analysis (SFA) principles. The cost frontier is used to establish the individual firm’s efficiency score during the period 2007-2010. Further analysis of the cost function shows that through asserting a second order polynomial time trend, a technological progress can be expected. However these results have been difficult to conclude as a result of the short time period. Other findings through the frontier estimation are that the individual firm did not improve their technological efficiency in the period. It is suggested that today’s regulatory model fail to induce Norwegian distribution companies to perform efficiently. Important theoretic concepts related to the regulatory model and frontier analysis have been elaborated.