To determine the relationship between magnetic memory signal and tensile stress and the influence of geometric size of the specimen on the surface magnetic field, static tensile tests on plate specimens made of Q345 low alloy steel with different thicknesses were performed. The variation regularities of surface magnetic signals of specimens with three thicknesses under different tensile stresses were investigated using the magnetometer TSC-1M-4. The test results show that the magnetic memory signal is positively correlated with tensile stress in the elastic stage but weakly correlated in the plastic stage. Compared with the normal component, the tangential component is more sensitive in characterizing the local yielding of the specimen. The early plastic deformation and stress concentration zone can be predicted via the abnormal magnetic change of the tangential component. Under the same stress level, the specimen thickness has a negative correlation with the surface magnetic intensity and no influence on the variation trend.