Material fatigue is an important issue in structural design, especially for aircraft that undergo long-term alternating stress. Composite materials have been used extensively in aircraft because of their high specific strength ratio. Using composites made from different reinforcing materials and matrices through various manufacturing methods can yield different levels of performance when structures undergo long-term cyclic stress. Currently, composite materials are extensively used to build aircraft for large commercial carriers such as the Boeing 787 and the Airbus A380. Composite materials are also used in newly-developed small business jets and light aircraft to reduce weight and fuel consumption. The primary objective of this study is to analyze the reaction of light aircraft landing gear under cyclic stress. This study uses finite element analysis software to conduct simulations, and compares the fatigue behavior of aluminum alloy and carbon fiber reinforced composites used in light sport aircraft (LSA) landing gear. We also explore the maximum stress, maximum strain and displacement of landing gear of different shapes (plate and column shapes). Among all the samples tested, column-shaped aluminum alloy landing gear has the lowest maximum stress under a static load; it also has the smallest maximum strain and y-axis displacement. However, column-shaped carbon fiber reinforced composites landing gear sustains approximately twice as much maximum stress under static loads and maximum alternating stress under fatigue loads than those made of aluminum alloy. All landing gear test samples can withstand cyclic stresses of over 108 cycles, except those made of aluminum alloy under 600 kg of load.