We present a near-infrared extinction study of the dark globule L694-2, a starless core that shows strong evidence for inward motions in molecular line profiles. The J,H, and K band data were taken using the European Southern Observatory New Technology Telescope. The best fit simple spherical power law model has index p=2.6 +/- 0.2, over the 0.036--0.1 pc range in radius sampled in extinction. This power law slope is steeper than the value of p=2 for a singular isothermal sphere, the initial condition of the inside-out model for protostellar collapse. Including an additional extinction component along the line of sight further steepens the inferred profile. Fitting a Bonnor-Ebert sphere results in a super-critical value of the dimensionless radius xi_max=25 +/- 3. The unstable configuration of material may be related to the observed inward motions. The Bonnor-Ebert model matches the shape of the observed profile, but significantly underestimates the amount of extinction (by a factor of ~4). This discrepancy in normalization has also been found for the nearby protostellar core B335 (Harvey et al. 2001). A cylindrical density model with scale height H=0.0164+/- 0.002 pc viewed at a small inclination to the cylinder axis provides an equally good radial profile as a power law model, and reproduces the asymmetry of the core remarkably well. In addition, this model provides a basis for understanding the discrepancy in the normalization of the Bonnor-Ebert model, namely that L694-2 has prolate structure, with the full extent (mass) of the core being missed by assuming symmetry between the profiles in the plane of the sky and along the line-of-sight. If the core is sufficiently magnetized then fragmentation may be avoided, and later evolution might produce a protostar similar to B335.

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