In this paper, we provide a comprehensive theoretical analysis of the electronic structure of InAs(111) surfaces with special attention paid to the energy region close to the fundamental bandgap. Starting from the bulk electronic structure of InAs calculated using the PBE functional with the inclusion of Hubbard correction and spin-orbit coupling, we derive proper values for the bandgap, split-off energy, as well as effective electron, light-hole and heavy-hole masses in full consistent with the available experimental results. Besides that we address the projected density of states associated with p orbitals of bulk indium and arsenic atoms. On the basis of optimized atomic surfaces we recover scanning tunneling microscopy images and calculate the band structure and orbital distributions of surface atoms, which along with accessible experimental data make it possible to speculate on the formation of the electron accumulation layer for both As- and In-terminated InAs(111) surfaces. Moreover, these results are accompanied by charge density distribution simulations.