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Statistically ion and electron densities are enhanced above strong crustal magnetic field regions according to measurements made by the Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft. Plasma created by ionization of neutrals in the lower ionosphere (where chemistry dominates) flows upward and becomes trapped on closed magnetic field loops. Enhanced ion density in the ionosphere (particularly O2+) is associated with enhanced photochemical escape of atomic oxygen. This paper presents a quasi‐1D multi‐fluid time‐dependent model of the Martian ionosphere for nine ion species. Ionospheric temperatures are adopted but ion densities and velocities (along the field lines) are determined using a numerical solution of the continuity and momentum equations. Diurnal effects are explored by varying photoionization rates. Three crustal field cases are considered: a low altitude closed, a high altitude closed, and a high altitude open field line. Additionally, a case with no crustal field is modeled to provide a comparison between regions with and without crustal fields in the upper Martian ionosphere. Model results show higher ion and electron densities in the crustal field cases than in the purely induced field case. Additionally, we find that densities are generally higher on the closed field lines than on the open field lines, and ion velocities are generally up the field lines, away from the Martian surface. We also find that velocities are larger on the open field line case. We compare modeled density results to MAVEN data and find general agreement. Implications for atmospheric escape, particularly photochemical escape of O, are also discussed. Plain Language Summary: Mars may not have a global magnetic field like the Earth, but it does have magnetic sources in its crust, giving rise to localized crustal magnetic fields. Previous spacecraft missions have measured increased ion and electron densities over regions where these crustal fields are strongest. This paper presents a model of ion flow along crustal fields at Mars, to try to explain the enhancement seen in data. Ion densities and velocities along crustal field lines are calculated. A diurnal (day to night) cycle is implemented to see how densities and velocities change throughout a Mars day. Multiple crustal field cases are modeled, as well as a generic "non‐crustal" ionosphere case. Modeled results show higher ion and electron densities in the crustal field line cases when compared to the non‐crustal case. Differences between modeled cases are compared with data results, and general agreement is evident. The effects of the modeled crustal fields on atmospheric escape are also discussed. Key Points: Plasma flows along Martian crustal magnetic field lines are modeled for nine ion speciesPlasma densities are higher for closed crustal magnetic fields than for open or induced fieldsUpward ion flow speeds are greater on open than on closed crustal magnetic fields [ABSTRACT FROM AUTHOR]