A DNA polymer with 1000 base pairs (bp’s) is modeled as an elastic rod at the base pair level. The elastic theory of rods is used to express the free energy of a double helix that has been deformed by stresses. After including a Lagrange multiplier in the energy expression to constrain the ends of the rod, an expression for the equilibrium configuration of the rod is obtained through the use of the appropriate Euler-Lagrange equations. The resulting set of differential equations is simplified to a set of nonlinear algebraic equations by discretizing the rod into individual elements. Because each element can have its own physical characteristics, base sequence effects can be taken into account. The methods developed are applied to DNA loops that are either nicked (i.e., torsionally relaxed) or unnicked (i.e., supercoiled). Small changes in the orientations and displacements of the ends of the loops can cause large changes in the overall configuration of the DNA. The nicked DNA shows a greater propensity to change configuration than the same unnicked DNA. DNA loops that contain regions of intrinsic curvature require less elastic energy for loop formation and facilitate conversion between different looped configurations.