Previous route choice studies treated uncertainties as randomness; however, it is argued that other uncertainties exist beyond random effects. As a general modeling framework for route choice under uncertainties, this paper presents a model of route choice that incorporates hyperpath and network generalized extreme-value-based link choice models. Accounting for the travel time uncertainty, numerical studies of specified models within the proposed framework are conducted. The modeling framework may be helpful in various research contexts dealing with both randomness and other non-probabilistic uncertainties that cannot be exactly perceived.