We use long-slit spectroscopic data to study in detail the extended narrow-line regions (ENLRs) of the Seyfert 1 galaxy ESO 362-G18 and Seyfert 2 galaxy ESO 362-G8. These two galaxies have similar emission-line luminosities and extents of the ENLR (D4 kpc), whose shapes in previous narrowband (O III) images suggest anisotropic escape of the nuclear ionizing radiation as expected for shadowing by a nuclear torus in the framework of the uni—ed model. In the Seyfert 1 galaxy the high-excitation gas shows an approximately cone-shaped morphology. From the observed kinematics, we conclude that the gas within the cone most probably belongs to the galaxy disk, which implies that the collimation axis is closer to the disk than half the opening angle of the cone of ionizing radiation. In the Seyfert 2 galaxy, the main structure in the high-excitation gas is an emission blob which apparently consists of a high- latitude cloud being blown away from the nuclear region and ionized by the nuclear source. We use the radial distribution of stellar population features in order to extrapolate this population to the nucleus and isolate the optical continuum of the nuclear source. We obtain a featureless power-law continuum for the Seyfert 1 galaxy, while for the Seyfert 2 galaxy we conclude that the F l P l~0.76 nuclear bluer color and smaller equivalent widths of the absorption lines are due to an aging burst of star formation (age B 300 Myr) and that the nuclear source is hidden from direct view. Using the photoionization code MAPPINGS Ic and a mixture of matter-bounded (MB) and ionization-bounded (IB) clouds, we model the ENLRs of the two galaxies. We use all the observables, mostly the emission-line —uxes as a function of distance from the nucleus and the optical nuclear contin- uum observed in the Seyfert 1 galaxy as well as its X-ray —ux, to constrain the parameters of a self- consistent model for the ENLR. For both galaxies, we conclude that a power-law ionizing continuum better reproduces the high-excitation lines near the nucleus than a multisegmented power law F l P l~1.2 used in previous works. For the Seyfert 1 galaxy ESO 362-G18, the inferred luminosity of the ionizing continuum can be reconciled with the —ux observed in the optical, while in the X-rays the observed —ux is D100 times weaker than that necessary to reproduce the line —uxes, suggesting that the X-ray contin- uum is absorbed toward Earth. For the Seyfert 2 galaxy ESO 362-G8, the inferred ionizing continuum when extrapolated to the optical implies a minimum obscuration toward the nuclear source of A V B 4.0 mag. In the hypothesis of an isotropic nuclear source, in order to better constrain the model parameters, we have adopted symmetrical physical conditions as a function of distance on both sides of the nucleus: namely, the ionizing —ux, the temperature, density, and ionization parameter of the MB gas, and the metallicity. The radial density behavior of the IB gas was observationally inferred from the (S II) doublet ratio. The only free parameter, which was allowed to vary independently, was the relative proportion of the MB and IB emission-line components along the ENLR. The high-excitation gas within the cone of ESO 362-G18 and within the blob of ESO 362-G8 have been modeled as regions of larger mass contri- bution from the MB component relative to other locations of the ENLR. We derive the —lling factors, covering factors, and gas masses along the ENLR as a function of dis- tance from the nucleus. A comparison between the model results for the two galaxies shows that, around the nucleus, the Seyfert 1 galaxy has a larger excitation due to a larger contribution of the MB com- ponent. However, in the cone, the excitation is lower than in the blob of the Seyfert 2 galaxy due to a combination of a lower ionizing —ux and larger gas density in the disk of the Seyfert 1 galaxy. The total ionized gas mass derived for the blob in the Seyfert 2 galaxy is 105.8 consistent with its proposed M _ , origin in a nuclear superwind which probably occurred D300 Myr ago, while the ionized gas mass in the disk of the Seyfert 1 galaxy is 1 order of magnitude smaller. Subject headings: galaxies: activegalaxies: ISMgalaxies: nucleigalaxies: Seyfert