Abstract We propose a computationally efficient platform for the analytical form-finding of tensegrity structures. The platform suggested utilizes the well-known Faddeev-LeVerrier algorithm to generate required relationships between force densities of elements providing explicit analytical conditions of self-stressed states. The method only requires sum and multiplications as major computational operations and bypasses complicated triangular factorizations and eigenvalue decompositions of the symbolic force density matrix. This makes our approach very efficient while enables us to employ powerful programs with symbolic math capabilities for the analytical form-finding. The viability and efficiency of the proposed method are demonstrated through examples of the analytical form-finding of some well-known tensegrities.