This paper is focused on the development of the new principles and operational algorithms of the transmission lines distance protection. The proposed distance protection algorithms utilize statistical information about the undefined and random parameters and quantities such as equivalent impedances of the systems at the unmonitored end of the power transmission line and current and voltage phasor measurements errors. Knowledge about the distribution of these parameters and values results in more secure and dependable procedure for the decision on the line tripping or restraining in case of the appearance of the fault conditions in the network. The proposed algorithm is based on the modeling of the faulted line and the Monte-Carlo method. The algorithm computes expected value of the distance to the fault, fault resistance in the fault point and the standard deviation of the distance to the fault. This leads to the inherent adaptive features of the approach.