A rubber composition for a solid golf ball contains a polybutadiene rubber component, a co-crosslinking agent, an organic peroxide, a filler, and an organic sulfur compound. When a core for a solid golf ball is formed by using the rubber composition for a solid golf ball, the content of a trans-structure in a cross-linked polybutadiene rubber component on the surface of the core is in a range of 20 to 39%, and a value obtained by subtracting the content of the trans-structure in the cross-linked polybutadiene rubber component at the center of the core from the content of the trans-structure in the cross-linked polybutadiene rubber component on the surface of the core is in a range of 5 to 35%. A solid golf ball produced by using such a core is excellent in hit feeling and flight characteristics. A method of producing a core for a solid golf ball makes it possible to simply produce the core specified as described above.