We investigate the interaction of edge dislocation in aluminum matrix with GP zones and θ″ phase with molecular dynamics (MD) simulations. All these copper-containing precipitates have a form of single or multilayer parallel copper disks separated by planes of aluminum atoms. The maximal number of copper layers of θ″ phase considered in the present work is equal to six; the diameter of precipitates varies from 3 to 15 nm. It is shown that all types of precipitates are initially overcome by dislocation with formation of the Orowan loop around them. The most fragile precipitate is GP zone of first type with a 3 nm diameter; it is sheared during the first closure of the Orowan loop by magnitude of leading partial dislocation, and obtains an additional displacement of trailing partial after the dislocation detachment. The remaining inclusions, even GP zones of a larger diameter, demonstrate the process of accumulation of surface deformation over time due to the shift of the upper half of the copper atom disks relative to the lower one. The moments of separation of the shifted halves are determined for different types of inclusion. Cutting of the strongest six-layer θ″ phase is not observed during our MD simulations. The evolution of local stress acting on copper atoms is traced over the several interactions required for the complete shearing of obstacle. The maximal local stress reached during deformation of GP of the first type of the smallest size is equal to 1.5 GPa, while the substantial increase in acting local stress is registered for higher number of copper disks. The local stress of 5.7 GPa is observed during the sequential interactions of dislocation with six-layer θ″ phase. The entire MD system demonstrate analogical growth of the average level of acting stress simultaneously with the increase in local stress on inclusion; it varies from about 125 MPa in the case of smallest GP zone to about 670 MPa for the hardest θ″ phase. The MD data is generalized in the form of the model of dislocation dynamics at interaction with precipitate. The model was previously proposed by Krasnikov and Mayer (2019) for the case of θ′ phase in aluminum. In the present work, it is modified by accounting the change in the energy of the dislocation core during contact with different types of inclusions. The energy values are fitted from a comparison of the time dependences of average stress in system with MD data. Variation of the core energy for the dislocation line segments attached to precipitate allows us to take into account specific features of precipitates with different number of layers.