A robot off-line simulation apparatus that allows a person to know an optimum placement for a robot, an operation margin index, etc. before going to an actual working site. Provisional robot placing positions are selected using data about a given sequence of task points (operation path), etc. The conditions for selection are (i) that solution to the inverse kinematics should be found regarding the entire sequence of task points, (ii) that the robot should not interfere with a peripheral device, and (iii) that regarding all the axes of the robot, the operation margin index should satisfy a criterion value. Simulation is performed according to operation programs under the condition that the robot is placed at each of the provisional placing positions, where data about cycle time, duty, energy value, change in acceleration/speed, etc. is collected. Using the collected data, evaluation of operation is performed regarding each of the provisional placing positions, and those provisional placing positions which allow good operation are identified as placing positions ensuring the robot operation. Further, using an evaluation function in which each aspect is given a weighting, the placing positions ensuring the robot operation are reduced to optimum placing positions ensuring the robot operation.