Abstract: In the present paper, a basic shape determination problem of cable frames is put forward and discussed. At first in the case of no self-equilibrated internal forces but with external loads, the continuous equilibrium equation of a single planar cable frame is given out on the basis of the balance of nodal forces. Then, this equation is extended to the case of exiting self-internal forces but without external loads. In the case of there are no self-internal forces within a cable frame, It will be necessary to assume a functional as the total strain energy of the upper and lower chord of a planar cable frame, the shape determination problem of cable frames will be a calculus of a variational problem with fixed boundary conditions and non-integral constraints. Then on the basis of Euler’s equation group the solution of this constrained calculus of variation can be derived out. Hopefully the work in the present paper could be helpful for practicing engineers and researchers.