The Space Weather program of the Latin American Giant Observatory (LAGO) Collaboration was designed to study the variation of the flux of atmospheric secondary particles at ground level produced during the interaction of cosmic rays with the air. This work complements and expands the inference capabilities of the LAGO detection network to identify the influence of solar activity on the particle flux, at places having different geomagnetic rigidity cut‐offs and atmospheric depths. This program is developed through a series of Monte Carlo sequential simulations to compute the intensity spectrum of the various components of the radiation field on the ground. A key feature of these calculations is that we performed detailed radiation transport computations as a function of incident direction, time, altitude, and latitude and longitude. Magnetic rigidity calculations and corrections for geomagnetic field activity are established by using the MAGNETOCOSMICS code, and the estimation of the flux of secondaries at ground level is implemented by using the CORSIKA code; thus, we can examine the local peculiarities in the penumbral regions with a more realistic description of the atmospheric and geomagnetic response in these complex regions of the rigidity space. As an example of our calculation scheme, we report some result on the flux at ground level for two LAGO locations: Bucaramanga, Colombia, and San Carlos de Bariloche, Argentina, for the geomagnetically active period of May 2005.