The present invention provides an offset printing blanket (10) or sleeve including one or more layers that are made with a soft thermoplastic polyurethane composition that provides excellent compression set and excellent resistance to apolar solvents, such as naphthenic mineral spirits. The subject invention more specifically reveals a printing blanket comprising: a base layer (12); a compressible layer (15), and a printing surface layer (18), wherein the compressible layer and/or the printing surface layer comprises a thermoplastic polyurethane composition, wherein the thermoplastic polyurethane composition made by reacting (a) at least one polyester polyol intermediate with (b) at least one diisocyanate and (c) at least one chain extender; wherein the polyester polyol intermediate comprises an intermediate derived from at least one dialkylene glycol and at least one dicarboxylic acid or an ester or anhydride thereof. It is particularly beneficial to utilize the thermoplastic polyurethane composition in the
