She completed her Ph.D. in 1992 in applied mathematics from Stony Brook University, under the joint supervision of Bradley J. Plohr and James Glimm.

She has most recently taught the undergraduate multivariable and vector calculus course at UC Berkeley.

[4] Čanić's research has involved the computational simulation of the stents used to treat arterial clogging.

By finding ways of simplifying computer models of stents from hundreds of thousands of nodes to only 400 nodes, she was able to make these simulations much more efficient, and used them to design improved stents that reduce clotting and scar formation.

[3] In 2014 she was elected as a fellow of the Society for Industrial and Applied Mathematics "for contributions to the modeling and analysis of partial differential equations motivated by applications in the life sciences.