This　study　proposes　a　new　car-following　model　that　considers　the　effects　of　two-sided　lateral　gaps　on　a　road　without　lane　discipline.　In　particular,　a　car-following　model　is　proposed　to　capture　the　impacts　from　the　lateral　gaps　of　the　leading　vehicles　on　both　sides　of　the　following　vehicle.　Linear　stability　analysis　of　the　proposed　model　is　performed　using　the　perturbation-method　to　obtain　the　stability　condition.　Nonlinear　analysis　is　performed　using　the　reductive　perturbation　method　to　derive　the　modified　Korteweg　de　Vries　equation　to　describe　the　density　wave　propagation.　Results　from　numerical　experiments　illustrate　that　the　proposed　car-following　model　has　larger　stable　region　compared　to　a　car-following　model　that　considers　the　effect　of　lateral　gap　on　only　one　side.　Also,　it　is　able　to　more　rapidly　dissipate　the　effect　of　a　perturbation　such　as　a　sudden　stimulus　from　a　leading　vehicle.　In　addition,　the　findings　of　this　study　provide　insights　in　analyzing　system　performance　of　a　non-lane-discipline　road　system　in　the　future.