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We present a new interval-based formulation for the static analysis of plane stress/strain problems with uncertain parameters in load, material and geometry. We exploit the Interval Finite Element Method (IFEM) to model uncertainties in the system. Overestimation due to dependency among interval variables is reduced using a new decomposition strategy for the structural stiffness matrix and the nodal equivalent load vector. Primary and derived quantities follow from minimization of the total energy and they are solved simultaneously and with the same accuracy by means of Lagrangian multipliers. Two different element assembly strategies are introduced in the formulation: one is Element-by-Element, and the other resembles conventional assembly. In addition, we implement a new variant of the interval iterative enclosure method to obtain outer and inner solutions. Numerical examples show that the proposed interval approach guarantees to enclose the exact system response.