Conversion of laser beam profiles is required in a wide variety of applications, such as producing a plane-parallel beam with a uniform intensity distribution. Traditional collimator systems are not capable of modifying the laser beam profile. High-quality uniformity of light can conveniently be achieved using high-order aspheric lens surfaces, which require expensive technology and equipment when they are manufactured from optical glass. A technique for using polymer optical materials for lens fabrication enables surfaces of any complexity to be obtained. In this paper, we describe the design of an aspheric-polymer-lens laser beam shaping system using ZEMAX software. We compare the quality parameters for systems using polymer optics and glass optics and provide recommendations for prudent selection of materials.