A new fully spherical multiple scattering Monte Carlo radiative transfer model named NIMO (NIWA Monte Carlo model) is presented. The ray tracing algorithm is described in detail along with the treatment of scattering and absorption, and the simulation of backward adjoint trajectories. The primary application of NIMO is the calculation of box-air-mass factors (box-AMFs), which are used to convert slant column densities (SCDs) of trace gases, derived from UV-visible multiple axis Differential Optical Absorption Spectroscopy (MAX-DOAS) measurements, into vertical column densities (VCDs). Box-AMFs are also employed as weighting functions for optimal estimation retrievals of vertical trace gas profiles from SCDs. Monte Carlo models are well suited to AMF calculations at high solar zenith angles (SZA) and at low viewing elevation angles where multiple scattering is important. Additionally, the object-oriented structure of NIMO makes it easily extensible to new applications by plugging in objects for new absorbing or scattering species. Box-AMFs and radiances, calculated for various wavelengths, SZAs, viewing elevation and azimuth angles and aerosol scenarios, are compared with results from nine other models using a set of exercises from a recent radiative transfer model intercomparison. NIMO results for these simulations are well within the range of variability of the other models.