To provide insight into the molecular mechanisms of local anesthetic action, we have carried out an extensive investigation of two amide type local anesthetics, lidocaine and articaine in both charged and uncharged forms, interacting with DMPC lipid membrane. We have applied both standard molecular dynamics simulations and metadynamics simulations to provide a detailed description of the free energy landscape of anesthetics embedded in the lipid bilayer. The global minimum of the free energy surface (equilibrium position of anesthetics in the lipid membrane) occurred around 1nm of the bilayer center. The uncharged anesthetics show more affinity to bind to this region compared to the charged drugs. The binding free energy of uncharged lidocaine in the membrane (-30.3kJ/mol) is higher than uncharged articaine (-24.0kJ/mol), which is in good agreement with higher lipid solubility of lidocaine relative to the articaine. The octanol/water partition coefficient of uncharged drugs was also investigated using expanded ensemble simulations. In addition, complementary standard MD simulations were carried out to study the partitioning behavior of multiple anesthetics inside the lipid bilayer. The results obtained here are in line with previously reported simulations and suggest that the different forms of anesthetics induce different structural modifications in the lipid bilayer, which can provide new insights into their complex membrane translocation phenomena.