A dual analog/digital model of the ascending path through the entire auditory periphery is described. The analog representation consists in the concatenation of electrical circuit submodels for (a) the diffraction of the external ear system; (b) the propagation through the concha and auditory canal; (c) the transmission through the middle ear; (d) the basilar membrane motion and cochlear hydrodynamics; (e) the fast motile mechanism of the outer hair cells; and (f) the neural transduction process of the inner hair cells. Time-domain numerical solutions are obtained by applying the technique of wave digital filtering onto the resulting analog circuit. The present version of the model reproduces the sound pressure gain at the eardrum for lateral sound incidence, the vibration characteristics of the stapes, and the low-frequency attenuation provided by the stapedial muscle. Source elements in the cochlear module provide level-dependent basilar membrane tuning curves leading to dynamic compression of input signals near the characteristic frequency/place. The output is the tonotopic distribution of firing activity in the auditory nerve. A companion article addresses the modeling of the descending paths [C. Giguere and P. C. Woodland, J. Acoust. Soc. Am. 94, 343-349 (1993)].