We report a molecular dynamics simulation of the influence of an Ar matrix on the relative stabilities of gauche- and s-cis-1,3-butadiene. Quantum-chemical investigations and most vapor-phase spectroscopic studies are in favor of a gauche-conformation for the second stable conformer of 1,3-butadiene. Ar matrix isolation studies with the aid of polarized FT-IR spectroscopy have, however, been interpreted in terms of a planar or effectively planar s-cis-structure. We investigated whether a surrounding matrix of Ar atoms changes the relative stabilities. The answer is positive: The s-cis-structure is stabilized by the matrix cage and the relative stabilities inverted. Whereas the torsional potential used for the isolated 1,3-butadiene has a lower energy for the gauche-conformation, the lowest energy s-cis-arrangement as found by simulating annealing turns out to be more stable than the gauche-structure in an Ar254 matrix.