The aim of this research was to define the compression strength of polylactic acid bolts produced using the fused deposition modelling method. In accomplishing this, static and cyclic compression tests for different metric thread sizes were carried out in accordance with ISO 4014. Tests were conducted on M42, M48, M56, M60, and M64 threads, while samples with three different types of pitch—one nominal and two fine threads—were prepared for each diameter. Standard ISO 604 for defining the compression modulus Ec was implemented as the test basis. Accordingly, the mean compression modulus value Ec for all measurements was 917.79 ± 184.99 MPa. Cyclic compression tests were then carried out on samples with the M64 × 4 thread. Fifty thread loading cycles were carried out for each variant to obtained different strain amplitude values and strain frequencies. Our work indicated that the values of the storage modulus defined in cyclic tests E′ increased, while the values of the loss modulus E″ decreased when the value of the strain frequency increased. We found it not possible to determine the nature of the changes in the value of the storage modulus E′ in the function of the strain amplitude. We did, however, observe an increase in the value of the loss modulus E″, together with the increase in the tested range of the strain amplitude. The determined mechanical values can be therefore be used for designing threaded connections made of polylactic acid using the fused deposition modelling method.