Allostery enables proteins to transmit local perturbations to distant functional residues, providing a biophysical basis for molecular signal integration. Here we introduce an Allosteric Logic Gate (ALG): an elastic network designed to convert two independent deformations at input sites into a Boolean-like conformational output at the distant active region. We model ligand binding as constrained local deformations at two spatially separated sites and read the output through a conformational measure at the active region. We show that it is possible to optimise the network's spring constants to produce a triggered allosteric response only when both inputs are present, thereby implementing a Boolean AND gate. Moreover, the evolved networks display a strongly non linear response, matching the switch-like property of logic gates. Statistical analysis of successful networks reveals conserved mechanical motifs, including stiff bonds connecting the input regions and flanking floppy regions that accommodate the output deformation. These results demonstrate that coarse-grained elastic networks can be inverse-designed to perform non-linear logic operations, suggesting a route toward programmable binary allostery, protein-inspired circuits, and biosensors capable of integrating multiple molecular signals.