Semiconductor nanowires based on non-nitride III-V compounds can be synthesized under certain growth conditions to favor the appearance of the wurtzite crystal phase. Despite reports in the literature of ab initio band structures for these wurtzite compounds, we still lack effective multiband models and parameter sets that can be simply used to investigate physical properties of such systems, for instance, under quantum confinement effects. In order to address this deficiency, in this study we calculate the ab initio band structure of bulk InAs and InP in the wurtzite phase and develop an 8 x 8 k . p Hamiltonian to describe the energy bands around the Gamma point. We show that our k . p model is robust and can be fitted to describe the important features of the ab initio band structure. The correct description of the spin-splitting effects that arise due to the lack of inversion symmetry in wurtzite crystals is obtained with the k-dependent spin-orbit term in the Hamiltonian, often neglected in the literature. All the energy bands display a Rashba-like spin texture for the in-plane spin expectation value. We also provide the density of states and the carrier density as functions of the Fermi energy. Alternatively, we show an analytical description of the conduction band, valid close to the Gamma point. The same fitting procedure is applied to the 6 x 6 valence band Hamiltonian. However, we find that the most reliable approach is the 8 x 8 k . p Hamiltonian for both compounds. The k . p Hamiltonians and parameter sets that we develop in this paper provide a reliable theoretical framework that can be easily applied to investigate electronic, transport, optical, and spin properties of InAs- and InP-based nanostructures.