Abstract： In the slab model the so-called universal modes are absolutly stable. How about the cylindrical plasma? The main difference is that instead of the out-going boundary condition in the slab mode, in the cylindrical plasma there is not any wave energy outgoing at r=0 and r=∞. This may change the stabilities of the modes effectively.Assuming exponential plasma density and current profiles, the integral eigen-equa-tion of drift wave has been derived. In the ease of slow radial variation, it can be converted into a second order differential equation. The equation has been solved numerically. The results show that the unstable modes do exist. The comparison between the two models (cylindrical one and slab one) has been made.