This paper solves a hard problem of uniform dimension for multi-parameter stable processes. More precisely, it is proved that if \(Z\) is a stable \((N,d,\alpha)\)-process and \(\alpha N\leq d\), then for all \(E\subset\mathbb R_+^N\), \(\dim Z(E)\alpha\dim E\) holds with probability 1, where \(Z(E)=\{x:\exists t\in E,\;Z_t=x\}\) is the image set of \(Z\) on \(E\). The uniform upper bounds for multi-parameter processes with independent increments, which may not possess the uniform stochastic Hölder condition, are also given. The results generalize the most of what proved before.