In a multi-piece solid golf ball having a core formed of a rubber composition, an intermediate layer formed of a polyurethane material and a cover, the ball satisfies the following condition: surface hardness of ball≤surface hardness of intermediate layer-encased sphere. When the ball is struck with a driver at a head speed of 40 m/s, the sum of the time t1 required from contact initiation between the driver and ball for deformation of the ball to reach a maximum value and the time t2 required from the state of maximum ball deformation for the ball and driver clubface to separate is at least 685 microseconds, and the ratio t2/t1 is at least 1.35, and the core has a specific hardness profile. This ball has an excellent flight performance when hit by low or moderate head-speed golfers, is receptive to spin on approach shots and has a good, soft feel at impact.