Magnetic resonance elastography (MRE) is commonly used as an image-based alternative for palpation of the internal organs of human body. The presence of tumor or other kind of pathologies in biological tissues can increase its stiffness. Therefore, while MRE technique is capable to provide a quantitative measurement, the qualitative description of the tissue stiffness could be potentially informative as well for physicians. MRE can be divided into several steps including the generation of waves in the tissue, measuring the field displacement of the tissue by magnetic resonance imaging devices, and then applying the constitutive based inversion algorithms to measure the material properties of the tissue. The inversion algorithms are dependent to the constitutive model in use, and moreover, it could be computationally expensive. To overcome this hindrance, in this paper, we propose a machine learning framework for categorizing the tissue stiffness based on the magnetic resonance elastography finite element simulation data. In our finite element simulation, the shear waves are generated in an axisymmetrical model by applying harmonic displacement at the center of the model with the known excitation frequency. To obtain the field displacement of the model, in the first step, the natural frequencies of the system will be calculated through numerical Block-Lanczos eigensolver algorithm. Thereafter, a transient dynamic modal analysis is carried out to find the corresponding displacement response of the tissue in different time steps of the simulation. To obtain the training dataset, ten simulations with the pre-assigned linear elastic modulus in the range of 2 to 6 kPa is conducted and the displacement of the tissue in three points at the end of the first and second cycle will be recorded as the features of the dataset. Each instance of the dataset is labelled as “Low“ or “High”, corresponding to its stiffness quantitative value lying in ranges of 2–4 kPa or 4–6 kPa. A machine learning classifying algorithm, a logistic regression hypothesis will be trained on this dataset. The trained hypothesis will be then tested on six new unseen simulation data with known elastic modulus values. The trained logistic regression was able to classify the tissue stiffness with the perfect accuracy score of 1.0. The findings of this study can be used for qualitative description of the tissue stiffness that can be beneficial for pathology diagnosis and moreover, it eliminates the need on the usage of inversion algorithms which leads to reduction in the computational complexity of tissue characterization.