Dual energy computed tomography (DECT) can provide simultaneous estimation of relative electron density rho(e) and effective atomic number Z(eff). The ability to obtain these quantities (rho(e), Z(eff)) has been shown to benefit selected radiotherapy applications where tissue characterization is required. The conventional analysis method (spectral method) relies on knowledge of the CT scanner photon spectra which may be difficult to obtain accurately. Furthermore an approximate empirical attenuation correction of the photon spectrum through the patient is necessary. We present an alternative approach based on a parameterization of the measured ratio of low and high kVp linear attenuation coefficients for deriving Z(eff) which does not require the estimation of the CT scanner spectra. In a first approach, the tissue substitute method (TSM), the Rutherford parameterization of the linear attenuation coefficients was employed to derive a relation between Z(eff) and the ratio of the linear attenuation coefficients measured at the low and high kVp of the CT scanner. A phantom containing 16 tissue mimicking inserts was scanned with a dual source DECT scanner at 80 and 140 kVp. The data from the 16 inserts phantom was used to obtain model parameters for the relation between Z(eff) and mu vertical bar(80kVp)(140kVp). The accuracy of the method was evaluated with a second phantom containing 4 tissue mimicking inserts. The TSM was compared to a more complex approach, the reference tissue method (RTM), which requires the derivation of stoichiometric fit parameters. These were derived from the 16 inserts phantom scans and used to calculate CT numbers at 80 and 140 kVp for a set of tabulated reference human tissues. Model parameters for the parameterization of mu vertical bar(80kVp)(140 kVp) were estimated for this reference tissue dataset and compared to the results of the TSM. Residuals on Z(eff) for the reference tissue dataset for both TSM and RTM were compared to those obtained from the spectral method. The tissue substitutes were well fitted by the TSM with R-2 = 0.9930. Residuals on Z(eff) for the phantoms were similar between the TSM and spectral methods for Z(eff) <8 while they were improved by the TSM for higher Z(eff). The RTM fitted the reference tissue dataset well with R-2 = 0.9999. Comparing the Z(eff) extracted from TSM and the more complex RTM to the known values from the reference tissue dataset yielded errors of up to 0.3 and 0.15 units of Z(eff) respectively. The parameterization approach yielded standard deviations which were up to 0.3 units of Z(eff) higher than those observed with the spectral method for Z(eff) around 7.5. Procedures for the DECT estimation of Z(eff) removing the need for estimates of the CT scanner spectra have been presented. Both the TSM and the more complex RTM performed better than the spectral method. The RTM yielded the best results for the reference human tissue dataset reducing errors from up to 0.3 to 0.15 units of Z(eff) compared to the simpler TSM. Both TSM and RTM are simpler to implement than the spectral method which requires estimates of the CT scanner spectra.