  In this paper we present a construction of stable bundles on Calabi-Yau
threefolds using the method of bundle extensions. This construction applies to
any given Calabi-Yau threefold with h^{1,1}>1. We give examples of stable
bundles of rank 2 and 4 constructed out of pure geometric data of the given
Calabi-Yau space. As an application, we find that some of these bundles satisfy
the physical constraint imposed by heterotic string anomaly cancellation.
