High frequency acoustic agitation is known to enhance chemical dissolution rates of patterned photoresists used in semiconductor and LIGA microdevice fabrication. To better understand the physical mechanism of this enhancement, we have developed analytical and numerical models of the acoustically induced steady streaming motion that transports dissolved polymer fragments from the bottom of trench-like features into the developer bath. Analytical solutions describing the time-periodic wave motion are used to evaluate the time-mean Reynolds stresses that drive the steady streaming motion. The resulting steady torroidal flow within the feature is computed by solving the Navier-Stokes equations, including either the acoustic Reynolds stresses or the slip velocity that applies when the acoustic boundary layers are sufficiently thin. The steady velocity field is then used to compute species transport by diffusion and advection. These numerical results are complemented by analytical solutions describing the dependence of enhanced transport on process parameters. The results indicate that acoustic streaming is probably responsible for the observed three to fourfold increase in development rates of LIGA features having widths of a few micrometers or more. To gain the same relative benefit in submicrometer features would, however, require use of frequencies and power levels more than tenfold greater than the conventional levels of 1 MHz and 10 W/cm(2).