Coherent synchrotron radiation (CSR) from a novel isochronous ring is a candidate for light source that provides THz radiation with high average flux. A compact isochronous accumulator ring (IAR) for the maximum beam energy of 54 MeV has been designed so as to eliminate the 0th order momentum compaction factor, and the 1st order of it is mostly compensated . In addition, the path length deviation due to betatron motion is mostly compensated in a cell. Though there is no RF cavity in IAR, the injected beam may circulate for certain number of turns. Multi experimental stations can be allocated like synchrotron radiation facilities. However, it has been well known that instability due to the CSR wake field is an issue for the beam stability in the ring operated at low alpha mode . Therefore, a study for effects of the CSR wake on the bunch length and shape in IAR has been in progress. It has turned out that the maximum longitudinal field strength created by CSR would be ∼ 0.15 MV/m for the case of 100 fs Gaussian bunch, which is considerably an intense field. To protect the bunch shape from the CSR wake, further study is definitely required.