Objective: In hypertension research aortic pressure wave travel and wave shape play a central role. Presently the explanation of aortic pressure is mainly based on wave travel and reflection in tube models with a single distal reflection. Increased pulse pressure with age is assumed to result from increased magnitude of distal reflection (higher SVR), and earlier return of the reflected wave (higher PWV). However, recent in vivo data show that the reflected wave runs towards the periphery rather than towards the heart as tube models predict. Approach: We analyzed wave travel and reflections in tube models in comparison with in vivo data. Main results: In the arterial system many reflection sites exist while tube models only have a single site. At all arterial locations, reflection is determined by the global reflection coefficient, given by local characteristic impedance and loading input impedance. The input impedance phase at low frequencies is negative causing delay between reflected and forward waves. Normalized impedances in the aorta depend much less on location than found in tube models. Therefore, the reflected pressure wave is delayed with respect to the forward wave and does not run towards the heart as predicted by tube models. Reflection mainly results from arterial stiffness and geometry, and arrival time of the reflected wave at the heart depends little on PWV. Increased SVR plays an indirect role: higher (transmural) pressure means stiffer vessels thereby affecting reflection. Significance: Tube models should not be used for interpretation of wave-phenomena and explanation of pressure wave shape.