[Object]The invention provides rubber compositions having excellent filler dispersibility, crosslinked products having excellent properties such as abrasion resistance, and tires that exhibit enhanced rolling resistance performance and attain simultaneous enhancements in steering stability and ice grip performance by virtue of using the compositions or the crosslinked products in portions of the tires.[Solution]The rubber composition includes 100 parts by mass of a solid rubber (A), 0.1 to 10 parts by mass of a modified liquid diene rubber (B) that is obtained by adding a modifying agent to an unmodified liquid diene rubber (B′) and has functional groups derived from the modifying agent, and 20 to 150 parts by mass of a filler (C). The modified liquid diene rubber (B) satisfies the following (i) to (iv): (i) the content of butadiene units is not less than 50 mass % relative to the total of all monomer units, (ii) the weight average molecular weight (Mw) is 25,000 to 120,000, (iii) the amount of the modifying agent added is 3 to 40 parts by mass per 100 parts by mass of the unmodified liquid diene rubber (B′), and (iv) the average number of functional groups per molecule of the modified liquid diene rubber (B) is 5 to 80.