We report studies on the extrusion of nearly monodisperse triblock and pentablock copolymers composed of poly(cyclohexylethylene) (C) and poly(ethylene) (E). Lamellae forming CEC triblock and CECEC pentablock copolymers were extruded through a slit die using a capillary rheometer at various processing speeds and temperatures below the order-disorder transition temperatures. Extrudate microstructure was characterized by small angle x-ray scattering and the surface characteristics were investigated by optical microscopy and profilometery. At low extrusion rates, the triblock and pentablock copolymers display different bulk orientation behavior, leading to relatively smooth surfaces in both cases. Above a characteristic wall shear stress, associated with a slope change in the flow curve, both polymers exhibit perpendicular lamellae alignment but dramatically different surface properties. The CEC material contains relatively low amplitude ( ∼ 1-3 μm) random roughness while the CECEC surface is highly textured, with periodic ∼ 50 μm undulations that resemble a sharkskin morphology. These differences are attributed to the rheological consequences of center C bridging in the pentablock copolymer.