Multi-piece solid golf ball

A multi-piece solid golf ball comprising a core, an intermediate layer encasing the core and a cover which encases the intermediate layer and has numerous dimples formed on an outside surface thereof (ball surface), wherein the core is formed of the rubber composition, the intermediate layer is formed of a resin material comprising an ionomer resin as a base resin and an inorganic granular filler, the cover is formed of a urethane resin material, the core has a diameter of at least 38.0 mm, the core has a deflection when compressed under a final load of 1,275 N (130 kgf) from an initial load of 98 N (10 kgf) of at least 3.9 mm, a sphere obtained by encasing the core with the intermediate layer (intermediate layer-encased sphere) has a surface hardness on the Shore D hardness scale of at least 69, the ball has a surface hardness on the Shore D hardness scale of 62 or less, the (intermediate layer thickness)/(core diameter) value is from 0.025 to 0.043, the (cover thickness)/(core diameter) value is from 0.014 to 0.027, and the intermediate layer has a specific gravity which is 1.05 or more.