The paper presents a method for constructing a set of vertical flight path segments, that would compose an aircraft's vertical flight envelope, by using an aircraft performance model. This method is intended to be used for aircraft flight plan prediction and optimisation algorithms. The goal is to reduce the volume of recurring segment performance computations currently required for flight plan prediction or optimisation. The method presented in this paper applies to a free-flight scenario. The flight-path segments composing the vertical flight envelope belong to one of the unrestricted climb, constant-speed level flight, step-climb and continuous descent segments, performed at the consigned climb, cruise and descent speed schedules and at the consigned air temperature values. The method employs an aircraft model using linear interpolation tables. Nine test scenarios were utilised to assess the performances of the resulting flight envelopes as a function of the number of cruise altitudes and descent flight paths. The set of evaluated performance parameters includes the range of total flight times and still-air flight distances, and the vertical profiles describing the minimum and maximum flight times, and still-air flight distances. The advantages of the proposed method are multiple. First, it eliminates the need for repetitive aircraft performance computations of identical vertical flight plan segments, and provides the means for quick retrieval of the corresponding performance data for use in the construction of a full flight plan. Second, the vertical flight path look-up structure and the vertical flight-path graph describe a set of vertical flight paths that consider an aircraft's and flight plan's configuration parameters and cover its maximum flight envelope. Third, the look-up structure and the graph provide the means for rapid and clear identification of the available options for constructing a flight-plan segment, as well as for detecting the points associated with changes in the flight phases, including climb, cruise, step-climb and descent.