Solar　radiation　may　be　shielded　by　the　terrain　relief　before　reaching　the　Martian　surface,　especially　over　some　rugged　terrains.　Yet,　to　date,　no　comprehensive　studies　on　the　spatial　structure　of　shielded　astronomical　solar　radiation　(SASR)　and　the　possible　sunshine　duration　(PSD)　on　Mars　have　been　conducted　by　previous　researchers.　Previous　studies　generally　ignored　the　influences　of　the　terrain　on　the　SASR　and　PSD,　which　resulted　in　a　corresponding　unexplored　field　on　SASR.　The　purpose　of　this　paper　is　to　study　the　Martian　spatial-temporal　structure　of　SASR　and　the　PSD　under　terrain　influences.　In　this　paper,　the　theory　of　Earth＇s　SASR,　the　previous　Martian　SASR　model　and　the　theory　of　planetary　science　were　combined　to　propose　the　SASR　model　that　can　be　applied　to　Mars.　Then,　with　the　spectrum　method　theory　of　geography,　we　defined　two　new　concepts　of　spectrums　to　explore　the　spatial-temporal　distribution　of　SASR　and　PSD　in　different　Martian　landforms.　We　found　SASR　and　PSD　on　Mars　were　significantly　influenced　by　terrain　relief　and　latitude　and　showed　sufficient　regularity,　which　can　be　concluded　as　a　gradual　attenuation　with　terrain　relief　and　a　regularity　of　latitude　anisotropy.　The　latitude　anisotropy　feature　is　a　manifestation　of　the　terrain　shielding　effect.　With　the　latitude　varying,　SASR　and　PSD　at　different　temporal　scale　generally　showed　different　features　with　those　of　Earth,　which　may　be　attributed　to　the　imbalanced　seasons　caused　by　Martian　moving　orbits　and　velocity.　Compared　to　PSD,　SASR　showed　more　regular　variation　under　terrain　relief　and　was　more　influenced　by　the　terrain　relief　which　revealed　that　SASR　is　more　sensitive　to　terrain　relief　than　PSD.　Additionally,　the　critical　area　is　a　quantitative　index　to　reflect　the　stable　spatial　structure　of　SASR　and　PSD　in　different　landforms　and　may　be　viewed　as　the　minimum　test　region　of　sample　areas.　The　corresponding　result　of　the　experiments　herein　indicated　that　either　spectrum　can　effectively　depict　the　spatial-temporal　distribution　of　SASR　and　PSD　on　Mars　under　terrain　relief　and　deepen　the　understanding　of　the　variation　of　SASR　and　PSD　influences　by　terrain.　The　critical　area　of　either　spectrum　can　be　employed　to　explore　and　determine　the　stable　spatial　structure　of　SASR　and　PSD　in　different　landforms.　The　proposed　Martian　SASR　model　and　the　new　spectral　method　theory　shed　new　light　on　revealing　the　spatial-temporal　structure　of　SASR　and　PSD　under　terrain　influences　on　Mars.