In order to analyze the influence of the noise on a cross-well traveltime tomography to detect a small scale low velocity body in a homogeneous medium, the first arrival travel times were computed one a tunnel model by a finite-difference ray tracing scheme. Three different types and four different intensity levels of white noises were added to the computed first arrival travel times, and velocity tomograms were constructed using an iterative inversion method (SIRT). Tomograms with the noise intensity up to 10% of the maximum traveltime delay in the tunnel model, showed the exact location of the tunnel. However, the velocity shown at the tunnel location was not close to air velocity but only slightly less than the velocity of the background medium. The additive random noise showed significantly less degree of influence on the resulting tomogram than the source- and receiver consistent noise.