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We study vector bundles on the moduli stack of elliptic curves over a localring R. If R is a field or a discrete valuation ring of (residue)characteristic not 2 or 3, all these vector bundles are sums of line bundles.For R the 3-local integers, we construct higher rank indecomposable vectorbundles and give a classification of vector bundles that are iteratedextensions of line bundles. For R the 2-local integers, we show that there areeven indecomposable vector bundles of arbitrary high rank.

Vector Bundles on the Moduli Stack of Elliptic Curves