A device for estimating the state quantity of a skid motion of a vehicle is provided with an element which finds road surface reaction force model values of respective wheels and a skid motion state quantity model value using a vehicle model including a friction characteristic model between the wheels and the road surface, an element which finds the deviation between the lateral acceleration model value generated in a predetermined position of the vehicle by the resultant force of the road surface reaction force model values and the lateral acceleration detected value indicated by the output of an actual lateral acceleration detecting means, and an element which determines, as the estimated value of the skid motion state quantity, a value obtained by adding a value obtained by passing the deviation through a filter having a high-cut characteristic to the skid motion state quantity model value.