The effect of agarose gel concentration and field strength on the electrophoretic trapping of open (relaxed) circular DNA was investigated using microscopic measurements of individual molecules stained with a fluorescent dye. Three open circles with sizes of 52.5, 115, and 220 kbp were trapped by the electric field (6 V/cm) and found to be predominately fixed and stretched at a single point in the gel. The length of the stretched circles did not significantly change with agarose concentration of the gels (mass fractions of 0.0025, 0.01, and 0.02). The relaxation kinetics of the trapped circles was also measured in the gels. The relaxation of the large open circles was found to be a slow process, taking several seconds. The velocity and average length of the 52.5 kbp open circles and 48.5 kbp linear DNA were measured during electrophoresis in the agarose gels. The velocity increased when the agarose concentrations were lowered, but the average length of the open-circle DNA (during electrophoresis) did not significantly change with agarose gel concentrations. The circles move through the gels by cycles of stretching and relaxation during electrophoresis. Linear dichroism was also used to investigate the trapping and alignment of the 52.5 kbp open circles. The results in this study provide information that can be used to improve electrophoretic separations of circular DNA, an important form of genetic material and commonly used to clone DNA.