The general static solutions of the scalar field equation for the potential V(φ) = - 1/2 M2φ2 + λ/4φ4 are determined for a finite domain in (1 + 1)-dimensional space-time. A family of real solutions is described in terms of Jacobi Elliptic Functions. We show that the vacuum-vacuum boundary conditions can be reached by elliptic cn-type solutions in a finite domain, such as that of the Kink, for which they are imposed at infinity. We prove uniqueness for elliptic sn-type solutions satisfying Dirichlet boundary conditions in a finite interval (box) as well the existence of a minimal mass corresponding to these solutions in a box. We defined expressions for the 'topological charge,' 'total energy' (or classical mass) and 'energy-density' for elliptic sn-type solutions in a finite domain. For large length of the box the conserved charge, classical mass and energy density of the Kink are recovered. Also, we have shown that using periodic boundary conditions the results are the same as in the case of Dirichlet boundary conditions. In the case of antiperiodic boundary conditions all elliptic sn-type solutions are allowed.151726452659Dashen, R., Hasslacher, B., Neveu, A., (1974) Phys. Rev., D10, p. 4131Mostepanenko, V.M., Trunov, N.N., (1997) The Casimir Effect and its Applications, , Oxford University Press, OxfordGradshteyn, I.S., Ryzhik, I.H., (1980) Table of Integrals, Series and Products, , Academic, New YorkAbramowitz, M., Stegun, I.A., (1972) Handbook of Mathematical Functions, , Dover Publications, New YorkDrazin, P.G., Johnson, R.S., (1989) Solitons: An Introduction, , Cambridge University Press, CambridgeRyder, L.H., (1988) Quantum Field Theory, , Cambridge University Press, CambridgeRajaraman, R., (1982) Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory, , North-Holland