This paper describes a method of modeling the motion uncertainty of moving obstacles and its application to mobile robot motion planning. The method explicitly considers three sources of uncertainty: path ambiguity, velocity uncertainty, and observation uncertainty. In the uncertainty model, the position of an obstacle at a certain time point is represented by a probabilistic distribution over possible positions on each possible path of the moving obstacle. Using this model, the best robot motion is selected in a decision-theoretic way. By considering the distribution, not the range, of uncertainty, more efficient behavior of the robot is realized.