  We analyze the tubular phase of self-avoiding anisotropic crystalline
membranes. A careful analysis using renormalization group arguments together
with symmetry requirements motivates the simplest form of the large-distance
free energy describing fluctuations of tubular configurations. The
non-self-avoiding limit of the model is shown to be exactly solvable. For the
full self-avoiding model we compute the critical exponents using an
epsilon-expansion about the upper critical embedding dimension for general
internal dimension D and embedding dimension d. We then exhibit various methods
for reliably extrapolating to the physical point (D=2,d=3). Our most accurate
estimates are nu=0.62 for the Flory exponent and zeta=0.80 for the roughness
exponent.
