Linear Fresnel reflector is one promising solar concentrating technology for medium and high temperatures (200-400 degrees C) because of its simple design and its low cost. However, the greatest drawback of this collector is the increased optical losses and thus the emphasis is usually given to this issue. In this direction, the objective of this work is the development of analytical expressions for the incident angle modifiers of a linear Fresnel reflector for the longitudinal and the transversal directions. The goal is to create a simple and accurate formula for all the possible solar angles ranges. The developed equations are based on reasonable assumptions and on the geometric analysis of a simple collector with flat primary mirrors. The developed equations are tested with literature data from other studies and from commercial collectors. It is found that the developed equations lead to accurate results with mean deviations up to 5%. The developed analytical expressions can be used for the quick calculation of the optical performance of a linear Fresnel reflector, as well as they can be used for the geometry optimization of the collector.