The fully intrinsic equations for beams comprise a relatively new set of equations for nonlinear modeling of structures comprised of beams. These equations are geometrically exact and constitute a closed set of equations even though they include neither displacement nor rotation variables. They do not suffer from the singularities and infinite-degree nonlinearities normally associated with finite rotation variables. In fact, they have a maximum degree of nonlinearity equal to 2. In spite of these and other advantages of these equations, using them for problems with certain boundary conditions may not be straightforward. This paper will examine the challenges of modeling various boundary conditions using fully intrinsic equations, thus helping future researchers to decide whether or not the fully intrinsic equations are suitable for solving a specific problem and elucidating pathways for their application to more general problems.