Generally, the finite element analysis of a structure is completed under deterministic inputs. However, uncertainties corresponding to geometrical dimensions, material properties, boundary conditions cannot be neglected in engineering applications. The probabilistic methods are the most popular techniques to handle these uncertain parameters but subjective results could be obtained if insufficient information is unavailable. Non-probabilistic methods can be alternatively employed, which has led to the procedures for non-probabilistic finite element analysis. Each non-probabilistic finite element analysis method consists of two individual parts, including the core algorithm and pre-processing procedure. In this context, three types of algorithms and two typical pre-processing procedures as well as their effectiveness are described in detail, based on which novel hybrid algorithms can be conceived for the specific problems and the future work in this research field can be fostered.