The most common way of production of sheath-core fibers is a technique where two polymer liquids are separately led to a position very close to the spinneret orifices and then extruded in sheath-core form. In the case of concentric fibers, the orifice supplying the "core" polymer is in the center of the spinning orifice outlet and flow conditions of core polymer fluid are strictly controlled to maintain the concentricity of both components when spinning. Eccentric fiber production is based on several approaches: eccentric positioning of the inner polymer channel and controlling of the supply rates of the two component polymers [8]; introducing a varying element near the supply of the sheath component melt [9]; introducing a stream of single component merging with concentric sheath-core component just before emerging from the orifice; and deformation of spun concentric fiber by passing it over a hot edge [10]. Other, rather different techniques to produce sheath-core fibers are coating of spun fiber by passing through another polymer solution [11] and spinning of copolymer into a coagulation bath containing aqueous latex of another polymer [12]. Modifications in spinneret orifices enable one to obtain different shapes of core or/and sheath within a fiber cross-section. There is considerable emphasis on surface tensions, viscosities and flow rates of component melts during spinning of these fibers.