Background: When performing the Upper Limb Neurodynamic Test 1 (ULNT1), the order of joint movement can be varied to place more stress onto certain nerve segments. However, the mechanisms underlying this phenomenon are still unclear. This study aimed to analyze the differences in the stiffness of the median nerve (MN) and the brachial plexus (BP) using ultrasound shear wave elastography during three sequences of the ULNT1: standard (ULNT1-STD), distal-to-proximal (ULNT1-DIST), and proximal-to-distal (ULNT1-PROX). Methods: Shear wave velocity (SWV) was measured at the initial and final position of each sequence at the MN (wrist) and at the C5 and C6 nerve roots (interscalene level) in 31 healthy subjects. Results: A significant interaction was found between ULNT1 sequence and location (p < 0.001). The ULNT1-STD and ULNT1-DIST induced a greater stiffness increase in the MN (5.67 ± 0.91 m/s, +113.94%; 5.65 ± 0.98 m/s, +115.95%) compared to C5 and C6 (p < 0.001). The ULNT1-PROX resulted in a significantly smaller increase in stiffness at the MN (4.13 ± 0.86 m/s, +54.17%, p < 0.001), but a greater increase at C5 (4.88 ± 1.23 m/s, +53.39%, p < 0.001) and at C6 (4.87 ± 0.81 m/s, +31.55%). The differences for the ULNT1-PROX at C6 were only significant compared to the ULNT1-STD (p < 0.001), but not the ULNT1-DIST (p = 0.066). Conclusions: BP and MN stiffness vary depending on the joint movement sequence during neurodynamic testing. However, the influence of the surrounding tissues may have affected SWV measurements; consequently, these results should be interpreted with caution.