A three-dimensional hierarchic finite element-based computational framework is developed for the investigation of inter-laminar stresses and displacements in composite laminates of finite width. As compared to the standard finite elements, hierarchic finite elements allow to change the order of approximation both locally and globally without modifying the underlying finite element mesh leading to very accurate results for relatively coarse meshes. In this paper, both symmetric cross-ply and angle-ply laminates subjected to uniaxial tension are considered as test cases. Tetrahedral elements are used for the discretisation of laminates and uniform or global p-refinement is used to increase the order of approximation. Each ply within laminates is modelled as a linear-elastic, homogenous and orthotropic material. With increasing the order of approximation, the developed computational framework is able to capture the complex profiles of inter-laminar stresses and displacements very accurately. Results are compared with reference results from the literature and found in a very good agreement. The computational model is implemented in our in-house finite element software library Mesh-Oriented Finite Element Method (MoFEM). The computational framework has additional flexibly of high-performance computing and makes use of the state-of-the-art computational libraries including Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Mesh-Oriented datABase (MOAB).