The production, attenuation, and absorption of secondary cosmic rays (SCR) are influenced by atmospheric parameters such as air pressure and temperature. To reliably correlate SCR flux measurements with atmospheric ionization driven by energetic particle precipitation, these dependencies must be quantified. Monte Carlo simulations enable detailed modeling of stochastic interactions between cosmic radiation and atmospheric components, providing a robust framework for analyzing underlying physical processes and predicting SCR flux under varying atmospheric conditions. This study introduces a simulation model based on the Monte Carlo N-Particle (MCNP) code, integrating atmospheric profiles from radiosonde data to model the production, absorption, and attenuation of SCR. The model's accuracy was validated through comparisons with the PHITS (Particle and Heavy Ion Transport code System)-based Analytical Radiation Model in the Atmosphere (PARMA) and experimental ground-based muon count measurements. It was subsequently used to investigate the dependence of muon flux on atmospheric pressure and temperature up to 20 km altitude. Results reveal a complex relationship between muon flux and atmospheric variables, particularly in the troposphere and lower stratosphere, where pressure correlations and barometric coefficients exhibit both positive and negative values depending on altitude. The model provides a valuable tool for investigating interactions between SCR and climate variables such as humidity and cloud coverage. Furthermore, the model can be coupled with dosimetry models to assess the biological effects of SCR, including deoxyribonucleic acid (DNA) damage, genomic instability, cellular dysfunction, and long-term health risks such as cancer.