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 a rubber composition that includes compounding ingredients (I) to (III),

• (I) a base rubber
• (II) an organic peroxide, and
• (III) water and/or a metal monocarboxylate,
• the intermediate layer is formed of a resin material, 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, and 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,
• wherein the rubber composition for the core further include (IV) sulfur, and the weight ratio between sulfur component of component (IV) and component (III), expressed as (IV)/(III) value, is from 0.010 to 0.200.