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.