We develop a dynamical coupled-channels model of K − p reactions, aiming at extracting the parameters associated with hyperon resonances and providing the elementary antikaon-nucleon scattering amplitudes that can be used for investigating various phenomena in the strangeness sector such as the production of hypernuclei from kaon-nucleus reactions. The model consists of (a) meson-baryon (M B) potentials v M ′ B ′ ,M B derived from the phenomenological SU(3) Lagrangian, and (b) vertex interactions Γ M B,Y * for describing the decays of the bare excited hyperon states (Y * ) into M B states. The model is defined in a channel space spanned by the two-bodyKN , πΣ, πΛ, ηΛ, and KΞ states and also the three-body ππΛ and πKN states that have the resonant πΣ * andK * N components, respectively. The resulting coupled-channels scattering equations satisfy the multichannel unitarity conditions and account for the dynamical effects arising from the offshell rescattering processes. The model parameters are determined by fitting the available data of the unpolarized and polarized observables of the K − p →KN, πΣ, πΛ, ηΛ, KΞ reactions in the energy region from the threshold to invariant mass W = 2.1 GeV. Two models with equally good χ 2 fits to the data have been constructed. The partial-wave amplitudes obtained from the constructed models are compared with the results from a recent partial-wave analysis by the Kent State University group. We discuss the differences between these three analysis results. Our results at energies near the threshold suggest that the higher partial waves should be treated on the same footing as the S wave if one wants to understand the nature of Λ(1405)1/2 − using the data below theKN threshold, as will be provided by the J-PARC E31 experiment.