In order to analyze the influences of assembly errors on the contact of roller enveloping worm gearing, an interference analysis model of the roller enveloping worm was build based on the theory of gear meshing and differential geometry, considering four assembly errors: center distance error, worm axial error, worm gear axial error, and shaft intersection angle error. The quantitative evaluation index and its numerical calculation method of the transmission pair under two kinds of interference conditions were put forward. The correctness of the mathematical model was verified by the example calculation. The results suggest that the theoretical contact line of the roller enveloping hourglass worm gearing is a space cylindrical spiral curve near the middle plane. Among the components of the assembly error, the axial error of the worm has the greatest influence on the contact interference, while the axial error of the worm gear has the least influence.