In this paper cylindrically symmetric vacuum solutions corresponding to generalized Einstein-Rosen-type gravitational waves are considered in the framework of Brans-Dicke (BD) scalar-tensor theory. We see that, similar to axially symmetric vacuum solutions, under some assumptions, it is possible to generate BD-vacuum solutions from corresponding solutions in general relativity. Using this generating technique, we present several exact solutions corresponding to soliton, standing or pulse waves in BD theory. We also present a Kasner-type time-dependent generalization of cylindrically symmetric static vacuum solution. Some physical implications of these solutions are discussed in some detail. The effect of pulse type waves on test particle motion is briefly discussed and compared with static vacuum background. We also see that, similar to general relativity, there are no trapped cylinders in Einstein-Rosen-type solutions in BD theory.