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. Calcareous sands are featured with higher peak internal friction angle and the variation of friction angle and dilation angle with strain in calcareous sands is also different from silica sands. In this paper, a large deformation finite element approach, the Arbitrary Lagrangian Eulerian method is used to study cone penetration in calcareous and silica sands. Frequent mesh generations are conducted to avoid distortion of soil elements around the cone tip. A modified Mohr-Coulomb constitutive model is introduced to describe the mobilized strength varied with plastic shear strain in calcareous and silica sands. The elastic and plastic parameters are 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. It demonstrates that the established numerical model has potential to capture the cone penetration in calcareous sands.