Disclosed is an alkylation reactor for preparing ethylbenzene. The reactor comprises a monolith catalyst system that includes a monolith support impregnated or co-formed with a catalyst suitable to catalyze the alkylation of benzene with ethylene. The catalyst may be selected from, for example, zeolites such as beta zeolite and MCM-22 zeolite, and fixed super acids. Also disclosed is a method of preparing ethylbenzene by alkylating a mixture of benzene and ethylene in an alkylation reactor comprising a monolith catalyst system, including a monolith support impregnated or co-formed with a suitable catalyst. In one embodiment the invention provides a convenient means of upgrading an existing reactor that has previously been used for conventional liquid phase alkylations such as those catalyzed by aluminum trichloride. The inventive alkylation method may be effectively and advantageously carried out under critical or near critical conditions, if desired.