The cone penetration test (CPT) is widely used to determine the mechanical properties of cohesionless soils. Most of the existing correlations were established in terms of silica sands, while the data for calcareous sands are limited. In comparison to silica sands, calcareous sands have a higher peak internal friction angle and the variation of the friction angle and the dilation angle with strain in calcareous sands is also different from silica sands. In this paper, the Arbitrary Lagrangian Eulerian method and a large deformation finite element approach, was used to study cone penetration in calcareous and silica sands. Frequent mesh generations were conducted to avoid the distortion of soil elements around the cone tip. A modified Mohr-Coulomb constitutive model was introduced to describe the mobilized strength varied with the plastic shear strain in calcareous and silica sands. The elastic and plastic parameters were determined by bender element tests and drained triaxial tests. Numerical results of cone tip resistance agree reasonably well with the existing data from centrifuge tests, showing that the established numerical model has the potential to simulate the cone penetration in calcareous sands.