We develop a systematic strong coupling approach for studying an extended t-V model with interactions of a finite range. Our technique is not based on the Bethe ansatz and is applicable to both integrable and non-integrable models. We illustrate our technique by presenting analytic results for the ground state energy (up to order 7 in t/V), the current density and density-density correlations for integrable and non-integrable models with commensurate filling factors. We further present preliminary numerical results for incommensurate non-integrable models.