Three rows of ball rolling grooves 23A to 23C are formed in each side of a guide rail 21, while being vertically arrayed. Three rows of ball rolling grooves 25A to 25C are also formed on the inner surface of each of the legs of a slider 22. The ball rolling grooves 25A to 25C are respectively disposed in opposition to the ball rolling grooves 23A to 23C to thereby form ball sliding passages 26A to 26C. In either of the upper or lower ball rolling passage 26A or 26C, each ball contacts, at four points, with the surfaces of the ball rolling groove 23A or 23C of the guide rail 21 and the ball rolling groove 25A or 25C of the slider 22. In the remaining ball rolling passages, each ball contacts at two points with the surfaces of the ball rolling grooves. One of lines L1 and L4, each of which connects two opposite contact points of those four ones in the upper or lower ball rolling passage is oriented in the same direction as of lines L2 and L3 connecting the contact points in the remaining ball rolling passages. With such a construction, the upper, medium and lower rows of ball trains receive all loads acting on the slider in share, whereby the linear guide assembly exhibits its maximum load capacity against the loads.