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We use the generalized Chowla-Selberg formula to consider the Casimir effectof a scalar field with a helix torus boundary condition in the flat($D+1$)-dimensional spacetime.  We obtain the exact results of the Casimir energy density and pressure forany $D$ for both massless and massive scalar fields. The numerical calculationindicates that once the topology of spacetime is fixed, the ratio of the sizesof the helix will be a decisive factor. There is a critical value $r_{crit}$ ofthe ratio $r$ of the lengths at which the pressure vanishes. The pressurechanges from negative to positive as the ratio $r$ passes through $r_{crit}$increasingly. In the massive case, we find the pressure tends to the result ofmassless field when the mass approaches zero. Furthermore, there is anothercritical ratio of the lengths $r_{crit}^{\prime}$ and the pressure isindependent of the mass at $r=r_{crit}^{\prime}$ in the D=3 case.

Casimir effect with a helix torus boundary condition