Robust and efficient full-field crystal plasticity models (based on finite element or FFT methods) have been developed over the past decades, and were extensively used for simulating and understanding different material phenomena at the macro- and mesoscales. On the other hand, nanoscale crystal plasticity models, which account for the effects of geometrically necessary dislocations (GNDs), are still significantly less developed. Different continuum non-local models were proposed in the literature, but most of them were not thoroughly verified against experimental and theoretical results. This work focuses on the Gurtin’s single crystalline strain gradient model. Herein, the thermodynamically consistent gradient model supplements the elastic strain energy density with a defect energy and the internal power with a contribution due to formation of shear gradients (conjugate to a microstress), which account for the effect of the GND densities. These newly added terms lead to introduction of a microstress in the constitutive equations, and require additional boundary conditions at the grain and phase boundaries. We show that the originally proposed quadratic defect energy leads to inaccurate predictions in the case of a double dislocation pile-up, and that the simple microstress interfacial constitutive relations proposed in the literature cannot accurately describe complex interfacial behavior. Thus, novel expression for the defect energy is proposed, leading to improved predictions in the case of the double dislocation pile-up. In addition, novel interfacial constitutive expressions are presented that describe the dislocation transmission/absorption at the interface more accurately. The initial boundary value problem is solved using a Green’s function method, where the convolution integral is efficiently calculated in the Fourier space (utilizing the convolution theorem). Main features of the numerical implementation are presented and discussed. The proposed model is applied to simulate mechanical tests on nano-metallic laminates, and the predictions are compared to experiments. The model predicts formation of a kink band under layer parallel compression, agreeing well with experimental observations. Process of kink band initiation and development, as predicted by the model, is also analyzed and described. It is found that dislocation pile-ups at the interfaces lead to activation of layer parallel slip systems, which in turn cause kink banding. Subsequently, the effect of novel defect energy and interfacial constitutive relations on the model predictions is analyzed.