In this paper, an analysis method and a measurement method for anisotropic magnetic shielding effectiveness (MSE) are discussed. Some magnetic sensors and memories require small magnetic shielded packages to decrease the influence of external magnetic noise. Whereas, the packages are applied for the external noise from various directions, sensitivity of the magnetic device in the package is affected by the direction and intensity of applied field noise. Influenced by the directions of external and internal magnetic fields, MSE of the shielded package varies several dozen decibels. Therefore, understanding the anisotropic MSE of the shielded package is indispensable for designing a shielded package that prevents malfunctions attributable to external magnetic noise. The $3 \times 3$ MSE matrix and the directivity of MSE are introduced as evaluation indicators of the anisotropic MSE. The MSE matrix and the directivity of MSE revealed that the MSE of the fabricated package varied significantly, from 24 dB to more than 60 dB, according to the direction of external field and internal field.