Ti-based shape memory alloys (SMAs) have been investigated as materials for medical devices and as a biomaterial that can be implanted in a living system as an alternative of any part. The behavior of such materials is evaluated by its activity, corrosion resistance, stability and compatibility with the living body. The direction of this paper is to deliver a brief description of the trends of corrosion in these materials. Titanium (Ti) shows satisfactory resistance to corrosion in natural and acidic environment but it has a trend toward corrosion in reducing acids. The shape memory alloys based on Ti are much favorable corrosion resistant materials to use in reducing acids. Normally human body fluid is analogous to a solution of about 0.9% NaCl which has a pH value 7.4. During surgery this value can be changed, with an increase of 7.8 and then dropping it to 5.5. Later some days the standard pH value of 7.4 can be re-gained. To evaluate corrosion rate of Ti based shape memory alloys in human body fluid, 0.9% NaCl solution was used as a medium. The basics of the shape memory material i.e. the mechanisms for shape memory, the shape memory effect and characterization of the evaluation of corrosion in systems based on Ti shape memory alloy is also reviewed in this article.