Alzheimer's disease (AD) is a neurodegenerative disorder and one of the main causes of dementia. The disease is associated with amyloid beta (Aβ) peptide aggregation forming initial clusters and then fibril structure and plaques. Other neurodegenerative diseases such as type 2 diabetes, amyotrophic lateral sclerosis, and Parkinson's disease follow a similar mechanism. Therefore, inhibition of Aβ aggregation is considered an effective way to prevent AD. Recent experiments have provided evidence that oligomers are more toxic agents than mature fibrils, prompting researchers to investigate various factors that may influence their properties. One of these factors is nanomechanical stability, which plays an important role in the self-assembly of Aβ and possibly other proteins. This stability is also likely to be related to cell toxicity. In this work, we compare the mechanical stability of Aβ-tetramers and fibrillar structures using a structure-based coarse-grained (CG) approach and all-atom molecular dynamics simulation. Our results support the evidence for an increase in mechanical stability during the Aβ fibrillization process, which is consistent with in vitro AFM characterization of Aβ42 oligomers. Namely, using a CG model, we showed that the Young modulus of tetramers is lower than that of fibrils and, as follows from the experiment, is about 1 GPa. Hydrogen bonds are the dominant contribution to the detachment of one chain from the Aβ fibril fragment. They tend to be more organized along the pulling direction, whereas in the Aβ tetramers no preference is observed.