The present invention relates to melt-spun polyurethane elastic fiber having a degree of luster of 70 or less, the degree of luster being defined as (I/Io).times.100 where the amount of light reflecting off the surface of the fiber is I and the amount of light reflecting off a standard white plate is Io. On the surface of preferable polyurethane elastic fiber, 10 or more mountain-like protrusions of 0.2 to 5.05 to 110 parts by weight of 5 to 110 parts by weight of .mu.m in height are present every 10 .mu.m fiber in the axial direction.Also, the present invention relates to a process for producing polyurethane elastic fiber, comprising melt-spinning butylene terephthalate-based crystalline polyester (A) and thermoplastic polyurethane (B) wherein before spinning, the compound (A) is melt-mixed with thermoplastic polyurethane (B-1) having isocyanate groups in an amount of 150 to 500 .mu.mol/g.Further, the present invention relates to covered fiber comprising the polyurethane elastic fiber as a core.Even if stockings, tights, sox etc. are produced using the covered fiber of the present invention, the luster phenomenon as the drawback of particularly melted spun urethane does not occur, so it is possible to obtain products with excellent appearance.