The paper introduces the R package FME, designed for inverse modelling, sensitivity analysis, and Monte Carlo analysis. FME is used to estimate parameters in mathematical models, particularly those involving differential equations, and to assess parameter identifiability and uncertainty. It includes functions for sensitivity analysis, parameter identifiability, model fitting, and Markov chain Monte Carlo (MCMC) methods to estimate parameter confidence intervals. The package is applied to a model describing the dynamics of the HIV virus, which involves three compartments: uninfected CD4+ T cells, infected CD4+ T cells, and free virions. The model is tested on simulated data with added noise to evaluate parameter estimation and sensitivity. FME provides tools for parameter calibration, sensitivity analysis, and uncertainty quantification, which are essential for understanding model behavior and making predictions. The package is also applicable to other types of models, not just those based on differential equations. The study highlights the importance of parameter identifiability and the challenges in estimating parameters when models are non-identifiable or when data are noisy. FME is shown to be effective in handling these challenges, providing robust methods for model fitting and uncertainty analysis. The paper also discusses the computational efficiency of FME and its suitability for dynamic simulations, emphasizing the importance of efficient algorithms and post-processing capabilities in R for mechanistic modelling.The paper introduces the R package FME, designed for inverse modelling, sensitivity analysis, and Monte Carlo analysis. FME is used to estimate parameters in mathematical models, particularly those involving differential equations, and to assess parameter identifiability and uncertainty. It includes functions for sensitivity analysis, parameter identifiability, model fitting, and Markov chain Monte Carlo (MCMC) methods to estimate parameter confidence intervals. The package is applied to a model describing the dynamics of the HIV virus, which involves three compartments: uninfected CD4+ T cells, infected CD4+ T cells, and free virions. The model is tested on simulated data with added noise to evaluate parameter estimation and sensitivity. FME provides tools for parameter calibration, sensitivity analysis, and uncertainty quantification, which are essential for understanding model behavior and making predictions. The package is also applicable to other types of models, not just those based on differential equations. The study highlights the importance of parameter identifiability and the challenges in estimating parameters when models are non-identifiable or when data are noisy. FME is shown to be effective in handling these challenges, providing robust methods for model fitting and uncertainty analysis. The paper also discusses the computational efficiency of FME and its suitability for dynamic simulations, emphasizing the importance of efficient algorithms and post-processing capabilities in R for mechanistic modelling.