Method for additive manufacturing a three-dimensional part in a layer-by-layer manner, wherein the method comprises (i) providing a carrier substrate to support the three-dimensional part and a print head connected to a reservoir of a printable composition; (ii) printing the printable composition with the print head in form of extrudate strands onto the carrier substrate to form a first layer; (iii) printing the printable composition with the print head in form of extrudate strand onto the first layer to form a second layer; (iv) optionally repeating step (iii) at least once to form a third or subsequent layer; (v) exposing the printable composition directly after printing and/or after each layer application and/or after application of multiple layer to radiation, preferably UV radiation; and (vi) curing the printed layers of the reactive curable printable composition to obtain the three-dimensional part; wherein the printable composition is a pasty polyurethane composition comprising - at least one polyisocyanate resin; - at least one monomer and/or prepolymer that is polymerizable by exposure to radiation, preferably an (meth)acrylate; and - at least one photoinitiator; wherein the pasty polyurethane composition has a viscosity factor (1,5/15) of at least 2 at application temperature, wherein the viscosity factor (1.5/15) represents the ratio of the viscosity measured at a shear rate of 1.5 s -1 and the viscosity measured at a shear rate of 15 s -1, using the method as set forth in BS EN ISO 3219:1995. wherein the method comprises (i) providing a carrier substrate to support the three-dimensional part and a print head connected to a reservoir of a printable composition; (ii) printing the printable composition with the print head in form of extrudate strands onto the carrier substrate to form a first layer; (iii) printing the printable composition with the print head in form of extrudate strand onto the first layer to form a second layer; (iv) optionally repeating step (iii) at least once to form a third or subsequent layer; (v) exposing the printable composition directly after printing and/or after each layer application and/or after application of multiple layer to radiation, preferably UV radiation; and (vi) curing the printed layers of the reactive curable printable composition to obtain the three-dimensional part; (i) providing a carrier substrate to support the three-dimensional part and a print head connected to a reservoir of a printable composition; (ii) printing the printable composition with the print head in form of extrudate strands onto the carrier substrate to form a first layer; (iii) printing the printable composition with the print head in form of extrudate strand onto the first layer to form a second layer; (iv) optionally repeating step (iii) at least once to form a third or subsequent layer; (v) exposing the printable composition directly after printing and/or after each layer application and/or after application of multiple layer to radiation, preferably UV radiation; and (vi) curing the printed layers of the reactive curable printable composition to obtain the three-dimensional part; wherein the printable composition is a pasty polyurethane composition comprising - at least one polyisocyanate resin; - at least one monomer and/or prepolymer that is polymerizable by exposure to radiation, preferably an (meth)acrylate; and - at least one photoinitiator; - at least one polyisocyanate resin; - at least one monomer and/or prepolymer that is polymerizable by exposure to radiation, preferably an (meth)acrylate; and - at least one photoinitiator; wherein the pasty polyurethane composition has a viscosity factor (1,5/15) of at least 2 at application temperature, wherein the viscosity factor (1.5/15) represents the ratio of the viscosity measured at a shear rate of 1.5 s -1 and the viscosity measured at a shear rate of 15 s -1, using the method as set forth in BS EN ISO 3219:1995.