Constipation will not cause high blood pressure, but they can be associated.

Constipation can occur for a number of reasons including dehydration, lack of fiber, some iron supplements, high progesterone levels, hypothyroidism, lack of intestinal flora and intestinal blockages.

Another cause is elevated serum calcium. Calcium causes muscles to stay contracted, including intestinal and arterial smooth muscles leading to constipation and high blood pressure. This is also why calcium channel blockers (CCBs) are the most commonly prescribed medication for high blood pressure. CCBs work by keeping calcium out of arterial muscles so they remain relaxed lowering the blood pressure.

Various things can raise serum calcium levels. The most common reasons for high calcium though are hyperparathyroidism (HPT) and pseudohyperparathyroidism (PHPT). Usually when I try to explain this to people I hear I had my thyroid checked and it was fine. The parathyroid glands though are not the same as the thyroid glands and have a different function.

HPT results from small benign tumors that form on the parathyroid glands. These lead to the overproduction of parathyroid hormone (PTH), which releases calcium from the bones raising serum calcium levels. These benign tumors are believed to form as a result of low serum vitamin D levels.

PHPT results from the excess consumption of phosphorus such as beef, dairy and colas. The elevated phosphorus levels are perceived as low serum calcium. This stimulates the release of PTH to release calcium from the bone to restore the proper calcium-phosphorus ratio.

Calcium supplementation is another common cause of elevated serum calcium. With all the hype around the myth that calcium treats osteoporosis people are tending to over do calcium supplementation and manufacturers are adding extra calcium to numerous products. Calcium needs to be balanced though with magnesium to prevent the adverse effects of too much calcium. These include constipation, high blood pressure, muscle spasms including spastic bladder and restless leg syndrome, brain fog, migraines, asthma, etc. Magnesium relaxes muscles by displacing calcium from the muscles. This is the basis of muscle movement. The influx of calcium contracts the muscles we need to contract to move limb for example. While magnesium relaxes the opposing muscles. The process then reverses in the muscles so the muscles can move in the other direction.

Ideally the ratio of calcium and magnesium in a supplement should be 1:1. In cases where calcium is high leading to problems such as high blood pressure or constipation the amount of magnesium should be slightly higher than the amount of calcium. Both should also be in an acidified for such as citrate or malate and not in the form of carbonates or oxides.

In and of itself, no. However pain, and associated straining can increase blood pressure.