Analytical formulae are used to calculate the phase variation alnd the slope parameter of the nucleon-nucleon (NN) scattering amplitude in terms of momentum transfer q2. An empirical series is presented to calculate the totalNNcross section. The proton-nucleus and nucleus-nucleus elastic differential cross-sections for different reactions at different bombarding energies less than 200 MeV/N have been calculated. The phase variation and the in-medium effect are considered in these calculations using the Glauber model. The calculated cross sections are in reasonable agreement with the experimental data over the whole range of energy considered in this work among light and medium nuclei