The quality of the rail passenger transport process depends on the technical parametersTechnical parameters of the railway track and the working condition of the train elementsElement. The condition of a railway track is indicated by theTrackquality index Track QualityRailwaytrack quality IndexRailwaytrack quality index. It evaluates the sum of the variationVariation of seven geometric parametersGeometric parameters. The quality model forTrainelements train elementsElement presented here, which is made up of 16 sub-criteriaSub-criteria, assesses trip durationTrip duration by train, the condition of the passenger carriageCarriage exteriorExterior, noiseNoiseinsulation reduction insulationInsulation, the interiorInterior of a passenger carriageCarriage, operation of ventilation, air conditioning, cooling and lightingLighting systems in terms of their timely on/off switching, temperatureTemperature control system for passenger carriageCarriage interiorInterior, the type and condition of the toilets on the train, the structure of berths and special facilities for people with disabilities. The model of the impact ofTrainelements train elementsElement on theQualityof the train journey quality of the train journeyJourney also assesses the availability of shower facilities that operate on a regular basis, bicycleBicycle and scooterScooter storage, availability of the smoking places, radio broadcasting unit and its centralized operation, availability of the dining-carDining-car, calling conductor to a passenger compartment in an emergency, use of electrical equipment on board the train. Using the data on the elementsElement of a specific international train and itsTrackquality index track quality indexQualityindex, a mathematical modelMathematical model has been developed to calculate the train quality index. The case presented shows that the model is correct as it gives a realistic result between 0 and 1.