The equilibriumEquilibrium of pre-solicited systems Systemspre-solicited subjected to incremental forcesIncremental forces is studied. According to the direct approachDirect approach of the Linearized TheoryLinearized theory, equilibrium is enforced in an adjacent configurationConfigurationadjacent, infinitely close to the pre-solicited configurationConfigurationpre-solicited. It is shown that, in addition to the elastic stiffness, a geometric stiffnessStiffnessgeometric appears, due to the disturbance of the pre-existing equilibrium triggered by the change of geometry. As alternatives to the direct approach, the Virtual Work FormulationVirtual Work Formulation and the Energy FormulationEnergy Formulation are discussed, whose forms differ from those of the linear theoryLinear theory in accounting for the pre-solicitation statePre-solicitationstate. Stiffening geometric contributions Geometric effectsstiffening are analyzed, which make the equilibrium of under-constrained systemsSystemsunder-constrained (as pendulums, string- or plate-like structures), which would be impossible in the reference configurationConfigurationreference, instead possible in the adjacent configuration. Softening geometric effectsGeometric effectssoftening are then studied, which are responsible for bifurcation of the equilibriumEquilibriumbifurcation, that occurs when a load multiplier of the pre-solicitation forces assumes a critical value. Here, the total stiffness matrix Matrixstiffness becomes singular, and the system loses stabilityStability, moving towards other stable positions (if any), to be determined by a nonlinear analysis. Imperfect systemsSystemsimperfect, i.e., affected by geometric defects or small incremental forces, are successively analyzed. For them, an approximate amplification ruleAmplification rule is stated, according to which the linear response in the pre-critical state is magnified by a factor which tends to infinity when the load multiplier approaches the critical value.