Using the Coulomb modified Glauber model, we analyze the elastic angular distribution and reaction (σ R ) and total (σ tot ) cross sections of K + -12 C at 635, 715, and 800 MeV/c, and of K + -40 Ca at 800 MeV/c. The basic (input) K + N amplitude is taken from the phase shift analysis, and for nuclear form factors we use the nucleon density distributions as obtained from the analyses of intermediate energy proton scattering experiments and the relativistic mean field (RMF) calculations. The analysis also considers the nuclear medium effects, and predicts the in-medium behavior of the K + N amplitude. We find that the elastic angular distribution is sensitive to the choice of the nucleon density distributions, whereas the nuclear medium effects are better seen in the study of reaction and total cross sections.