Abstract The σ expansion and the linear σ expansion are analytical perturbation techniques that enable one to find approximate analytic solutions to nonlinear problems. These expansions, augmented by new variational strategies, often yield excellent results already in first order. We study in this paper the static kinks in scalar field theories with V[φ] = - 1 2 m 2φ 2 + gφ 2n using these techniques. We find excellent agreement between the lowest order variational approximation in both methods and the exact answer. We also estimate the energy of the first excited quantum state by considering small oscillations about the kink motion and using our variational wave functions and a shape parameter ansatz for the first excited state wave function.