1-butene based polymer satisfying following requirements (1″) to (4″) provides formed product having low stickiness, superior flexibility and transparency. (1″) Crystalline resin having melting point (Tm−P), not observed or in the range of 0 to 100° C., wherein said melting point defined as the peak top of the peak observed in the highest temperature zone of the melting heat absorption curve obtained by heating a sample of said polymer at a rate of 10° C./minute using Differential Scanning Calorimeter (DSC), after melting said sample in advance at 190° for 5 minutes under nitrogen atmosphere, followed by cooling it to −10° C. at a rate of 5° C./minutes, and keeping it at −10° C. for 5 minutes. (2″) Stereoregularity index {(mmmm)/(mmrr+rmmr)} is at most 20. (3″) Molecular weight distribution (Mw/Mn) measured by Gel Permeation Chromatography (GPC) method is at most 4.0. (4″) Weight average molecular weight (Mw) measured by GPC method is in the range of 10,000 to 1,000,000.