We present new theoretical stellar yields and surface abundances for asymptotic giant branch ( AGB ) models with a metallicity appropriate for stars in the Small Magellanic Cloud ( SMC , Z = 0.0028 , [ Fe/H ] \approx - 0.7 ) . New evolutionary sequences and post-processing nucleosynthesis results are presented for initial masses between 1 { M } _ { \odot } and 7 { M } _ { \odot } , where the 7 { M } _ { \odot } is a super-AGB star with an O-Ne core . Models above 1.15 { M } _ { \odot } become carbon rich during the AGB , and hot bottom burning begins in models M \geq 3.75 { M } _ { \odot } . We present stellar surface abundances as a function of thermal pulse number for elements between C to Bi and for a selection of isotopic ratios for elements up to Fe and Ni ( e.g. , ^ { 12 } { C } / ^ { 13 } { C } ) , which can be compared to observations . The integrated stellar yields are presented for each model in the grid for hydrogen , helium and all stable elements from C to Bi . We present evolutionary sequences of intermediate-mass models between 4–7 { M } _ { \odot } and nucleosynthesis results for three masses ( M = 3.75 , 5 , 7 { M } _ { \odot } ) including s -process elements for two widely used AGB mass-loss prescriptions . We discuss our new models in the context of evolved AGB stars and post-AGB stars in the Small Magellanic Clouds , barium stars in our Galaxy , the composition of Galactic globular clusters including Mg isotopes with a similar metallicity to our models , and to pre-solar grains which may have an origin in metal-poor AGB stars .