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We determine the distances to 18 galaxy clusters with redshifts ranging fromz~0.14 to z~0.78 from a maximum likelihood joint analysis of 30 GHzinterferometric Sunyaev-Zel'dovich effect (SZE) and X-ray observations. Wemodel the intracluster medium (ICM) using a spherical isothermal beta model. Wequantify the statistical and systematic uncertainties inherent to these directdistance measurements, and we determine constraints on the Hubble parameter forthree different cosmologies. These distances imply a Hubble constant of 60 (+4,-4) (+13, -18) km s-1 Mpc-1 for an Omega_M = 0.3, Omega_Lambda = 0.7 cosmology,where the uncertainties correspond to statistical followed by systematic at 68%confidence. With a sample of 18 clusters, systematic uncertainties clearlydominate. The systematics are observationally approachable and will beaddressed in the coming years through the current generation of X-raysatellites (Chandra & XMM-Newton) and radio observatories (OVRO, BIMA, & VLA).Analysis of high redshift clusters detected in future SZE and X-ray surveyswill allow a determination of the geometry of the universe from SZE determineddistances.Comment: ApJ Submitted; 40 pages, 9 figures (fig 3 B&W for size constraint),  13 tables, uses emulateapj5 styl

Determining the Cosmic Distance Scale from Interferometric Measurements of the Sunyaev‐Zeldovich Effect