In this study, two versions of non-imaging dish reflectors designed for providing uniform flux profiles on the receiver are proposed. These two reflectors, namely Type I and Type II, are designed according to two different ray routes and described by differential equations. Both the reflectors are determined by three dimensionless parameters: bottom opening diameter, receiver diameter, and the distance from the bottom to the receiver. By using ray tracing technique, radiation flux distributions on the receivers of these non-imaging reflectors are investigated. The results suggest that for concentrating collimated incidence, both the two non-imaging concentrating reflectors have good performance in terms of concentrated flux uniformity on the receiver. However, the Type I reflectors present more uniform flux maps than Type II reflectors for concentrating solar rays. It is also concluded that the value of the distance from the bottom to the receiver has an effect on the angle between the incident ray and the reflected ray, which is relative to the performance of concentrating solar rays. Bottom opening diameter and receiver diameter function to codetermine the geometrical concentration ratio (CR) of the reflectors. (C) 2014 Elsevier Ltd. All rights reserved.