The neutron flux is a crucial parameter for the analysis of nuclear reactors, because it affects the reaction rate and thus the fuel burnup. Moreover, a very precise knowledge of the flux in the irradiation positions is helpful for benchmarking the simulation models of the reactor. In particular, an MCNP model of the TRIGA Mark II reactor installed at LENA (Laboratory of Applied Nuclear Energy) of the University of Pavia was developed in the recent years, describing the geometries and the materials of the whole reactor with very good accuracy. In this article, we present the results of the neutron flux measurements in four irradiation positions. The neutron activation technique was used to perform an absolute measurement of the flux. Various samples containing a known amount of elements were irradiated in the reactor facilities and the activation rate of a large number of isotopes was measured through γ-ray spectroscopy with very low background HPGe detectors. In order to accurately calculate the activation rate, Monte Carlo codes based on GEANT4 were developed to evaluate the γ-ray detection efficiency for every radioisotope of interest. The samples were measured with three different HPGe detectors and the measurements were repeated in various geometric configurations in order to assess the reliability and repeatability of this analysis technique. The MCNP reactor model was used to evaluate the energetic neutron flux distributions in the irradiation positions. The effective activation cross sections were computed from these distributions, testing the dependence on the MCNP simulation results. Finally, the neutron flux was calculated from the data of activation rate and effective cross section of each isotope. The good agreement in the results of the flux calculations from the many different activated samples confirms the reliability of the adopted methodology.